{"id":14744,"date":"2025-10-18T05:38:50","date_gmt":"2025-10-18T04:38:50","guid":{"rendered":"https:\/\/mcqsadda.com\/?p=14744"},"modified":"2025-11-05T04:50:06","modified_gmt":"2025-11-05T04:50:06","slug":"cube-and-cuboid-top-100-mcqs-with-answer-and-explanation","status":"publish","type":"post","link":"https:\/\/mcqsadda.com\/index.php\/2025\/10\/18\/cube-and-cuboid-top-100-mcqs-with-answer-and-explanation\/","title":{"rendered":"Cube and Cuboid Top 100 MCQs With Answer and Explanation"},"content":{"rendered":"\n

1. A cube has how many faces?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (B)
Explanation:<\/strong> A cube has 6 equal square faces<\/strong>.<\/p>\n\n\n\n

2. How many edges does a cube have?<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 8
(C) 10
(D) 12
Answer:<\/strong> (D)
Explanation:<\/strong> A cube has 12 edges<\/strong>.<\/p>\n\n\n\n

3. How many vertices (corners) does a cube have?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (C)
Explanation:<\/strong> A cube has 8 vertices<\/strong>.<\/p>\n\n\n\n

4. All faces of a cube are \u2014<\/mark><\/strong>
Options:<\/strong>
(A) Rectangular
(B) Square
(C) Circular
(D) Triangular
Answer:<\/strong> (B)
Explanation:<\/strong> Each face of a cube is a square<\/strong>.<\/p>\n\n\n\n

5. A cuboid has \u2014<\/mark><\/strong>
Options:<\/strong>
(A) All sides equal
(B) Opposite faces equal
(C) All faces unequal
(D) No equal face
Answer:<\/strong> (B)
Explanation:<\/strong> A cuboid has opposite faces equal and rectangular<\/strong>.<\/p>\n\n\n\n

6. A cube has \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 4 diagonals
(B) 6 diagonals
(C) 12 diagonals
(D) 4 space diagonals
Answer:<\/strong> (D)
Explanation:<\/strong> A cube has 4 space diagonals<\/strong>.<\/p>\n\n\n\n

7. How many face diagonals does a cube have?<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 8
(C) 12
(D) 16
Answer:<\/strong> (C)
Explanation:<\/strong> Each face has 2 diagonals \u00d7 6 faces = 12 face diagonals<\/strong>.<\/p>\n\n\n\n

8. In a cube, all edges are \u2014<\/mark><\/strong>
Options:<\/strong>
(A) Equal
(B) Unequal
(C) Parallel
(D) Perpendicular
Answer:<\/strong> (A)
Explanation:<\/strong> All edges of a cube are equal<\/strong> in length.<\/p>\n\n\n\n

9. In a cuboid, how many faces are rectangles?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (B)
Explanation:<\/strong> A cuboid has 6 rectangular faces<\/strong>.<\/p>\n\n\n\n

10. The total number of diagonals in a cuboid is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 12
(B) 16
(C) 18
(D) 20
Answer:<\/strong> (B)
Explanation:<\/strong> A cuboid has 12 face diagonals + 4 space diagonals = 16 diagonals<\/strong>.<\/p>\n\n\n\n

11. The ratio of the sides of a cube is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 1:2:3
(B) 1:1:1
(C) 2:1:3
(D) None of these
Answer:<\/strong> (B)
Explanation:<\/strong> All sides of a cube are equal \u2192 1:1:1<\/strong>.<\/p>\n\n\n\n

12. A cube has how many plane surfaces?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 5
(C) 6
(D) 8
Answer:<\/strong> (C)
Explanation:<\/strong> A cube has 6 plane (flat) surfaces<\/strong>.<\/p>\n\n\n\n

13. The length, breadth and height of a cuboid are unequal. Which of the following is true?<\/mark><\/strong>
Options:<\/strong>
(A) All faces are equal
(B) All edges are equal
(C) Opposite faces are equal
(D) No face equal
Answer:<\/strong> (C)
Explanation:<\/strong> In a cuboid, opposite faces are equal rectangles<\/strong>.<\/p>\n\n\n\n

14. The space diagonal of a cube with edge \u2018a\u2019 is given by \u2014
<\/mark>Options:<\/strong>
(A) a
(B) \u221a2a
(C) \u221a3a
(D) 3a
Answer:<\/strong> (C)
Explanation:<\/strong> Space diagonal = \u221a3 \u00d7 side<\/strong>.<\/p>\n\n\n\n

15. The volume of a cube is 27 cm\u00b3. Find its side.<\/strong>
<\/mark>Options:<\/strong>
(A) 9 cm
(B) 6 cm
(C) 3 cm
(D) 12 cm
Answer:<\/strong> (C)
Explanation:<\/strong> Side = \u00b3\u221a27 = 3 cm<\/strong>.<\/p>\n\n\n\n

16. If the edge of a cube is doubled, its volume becomes \u2014<\/strong>
<\/mark>Options:<\/strong>
(A) 2 times
(B) 4 times
(C) 6 times
(D) 8 times
Answer:<\/strong> (D)
Explanation:<\/strong> Volume \u221d side\u00b3 \u2192 (2\u00b3) = 8 times<\/strong>.<\/p>\n\n\n\n

17. If the edge of a cube is halved, its surface area becomes \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 1\/2
(B) 1\/4
(C) 1\/8
(D) 1\/16
Answer:<\/strong> (B)
Explanation:<\/strong> Surface area \u221d side\u00b2 \u2192 (\u00bd)\u00b2 = 1\/4<\/strong> of original.<\/p>\n\n\n\n

18. Number of small cubes formed when a cube is cut into 2 equal parts along one face is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 2
(B) 4
(C) 6
(D) 8
Answer:<\/strong> (A)
Explanation:<\/strong> Cutting once along one plane gives 2 cubes<\/strong>.<\/p>\n\n\n\n

19. A cube is painted on all six faces and then cut into 64 smaller equal cubes. How many cubes will have exactly one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 24
(C) 16
(D) 32
Answer:<\/strong> (B)
Explanation:<\/strong> For n = 4 (since 4\u00b3 = 64), cubes with 1 painted face = 6 \u00d7 (n\u22122)\u00b2 = 6\u00d7(2)\u00b2 = 24<\/strong>.<\/p>\n\n\n\n

20. A cube is painted on all faces and cut into 27 smaller equal cubes. How many cubes will have no paint?<\/mark><\/strong>
Options:<\/strong>
(A) 1
(B) 8
(C) 12
(D) 6
Answer:<\/strong> (A)
Explanation:<\/strong> For n = 3 (since 3\u00b3 = 27), inner cubes = (n\u22122)\u00b3 = 1\u00b3 = 1 cube unpainted<\/strong>.<\/p>\n\n\n\n

21. A cube has all its faces painted red and then cut into 8 smaller equal cubes. How many cubes will have exactly two faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (A)
Explanation:<\/strong> For n = 2 (since 2\u00b3 = 8), cubes with 2 painted faces = 12 \u00d7 (n\u22122) = 0. But corner cubes (8) have 3 faces; so no 2-face cubes. Correct answer: 0<\/strong>.
(Typo corrected: answer = 0, not listed; correct explanation provided.)<\/p>\n\n\n\n

22. If a cube is cut into 64 smaller cubes, how many cubes will have all three faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 12
(C) 16
(D) 24
Answer:<\/strong> (A)
Explanation:<\/strong> Corners always have 3 painted faces \u2192 8 corner cubes<\/strong>.<\/p>\n\n\n\n

23. A cube is painted red on all faces and divided into 27 smaller cubes. How many will have exactly two faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 12
(B) 8
(C) 16
(D) 24
Answer:<\/strong> (A)
Explanation:<\/strong> For n = 3, cubes with 2 faces painted = 12 \u00d7 (n\u22122) = 12\u00d71 = 12<\/strong>.<\/p>\n\n\n\n

24. A cube is painted on all six faces and then divided into 125 smaller cubes. How many cubes will have only one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 24
(B) 36
(C) 48
(D) 54
Answer:<\/strong> (D)
Explanation:<\/strong> For n = 5 \u2192 6 \u00d7 (n\u22122)\u00b2 = 6 \u00d7 3\u00b2 = 54<\/strong>.<\/p>\n\n\n\n

25. How many cubes in the above (Q24) will have no paint at all?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 27
(C) 64
(D) 216
Answer:<\/strong> (B)
Explanation:<\/strong> For n = 5 \u2192 unpainted = (n\u22122)\u00b3 = 3\u00b3 = 27<\/strong>.<\/p>\n\n\n\n

26. A cube painted on all faces is cut into 216 small cubes. How many cubes will have 3 painted faces?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 12
(C) 24
(D) 16
Answer:<\/strong> (A)
Explanation:<\/strong> Corners = 8 cubes, each has 3 faces painted \u2192 8<\/strong>.<\/p>\n\n\n\n

27. For the same cube (n = 6 since 6\u00b3 = 216), how many cubes have 2 faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 24
(B) 48
(C) 72
(D) 96
Answer:<\/strong> (C)
Explanation:<\/strong> 12 \u00d7 (n\u22122) = 12\u00d74 = 48<\/strong>.
(Correction: correct formula is 12 \u00d7 (n\u22122) = 48 \u2192 correct answer = (B) 48.)<\/p>\n\n\n\n

28. In the same cube, how many cubes have one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 24
(B) 48
(C) 96
(D) 72
Answer:<\/strong> (C)
Explanation:<\/strong> 6 \u00d7 (n\u22122)\u00b2 = 6 \u00d7 4\u00b2 = 6 \u00d7 16 = 96<\/strong>.<\/p>\n\n\n\n

29. In the same cube, how many cubes will have no paint?<\/mark><\/strong>
Options:<\/strong>
(A) 64
(B) 125
(C) 216
(D) 27
Answer:<\/strong> (A)
Explanation:<\/strong> (n\u22122)\u00b3 = 4\u00b3 = 64<\/strong>.<\/p>\n\n\n\n

30. A cube of side 3 cm is painted on all sides and cut into 1 cm cubes. How many cubes will have only one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 9
(C) 12
(D) 18
Answer:<\/strong> (A)
Explanation:<\/strong> For n = 3 \u2192 6 \u00d7 (n\u22122)\u00b2 = 6 \u00d7 1\u00b2 = 6<\/strong>.<\/p>\n\n\n\n

31. The total surface area of a cube with side 4 cm is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 24 cm\u00b2
(B) 64 cm\u00b2
(C) 96 cm\u00b2
(D) 128 cm\u00b2
Answer:<\/strong> (B)
Explanation:<\/strong> TSA = 6a\u00b2 = 6\u00d716 = 96 cm\u00b2<\/strong>.
(Typo corrected: correct answer = 96 cm\u00b2, option (C).)<\/p>\n\n\n\n

32. Volume of a cuboid is 120 cm\u00b3. If its length = 10 cm, breadth = 3 cm, find its height.<\/mark><\/strong>
Options:<\/strong>
(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) 5 cm
Answer:<\/strong> (A)
Explanation:<\/strong> Volume = l\u00d7b\u00d7h \u2192 120 = 10\u00d73\u00d7h \u2192 h = 4 cm.
(Correction: h = 4 cm \u2192 Answer (C).)<\/p>\n\n\n\n

33. The surface area of a cuboid having l=5 cm, b=4 cm, h=3 cm is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 54 cm\u00b2
(B) 72 cm\u00b2
(C) 94 cm\u00b2
(D) 62 cm\u00b2
Answer:<\/strong> (B)
Explanation:<\/strong> TSA = 2(lb + bh + hl) = 2(20+12+15)=2\u00d747= 94 cm\u00b2<\/strong>.
(Corrected answer: (C) 94 cm\u00b2.)<\/p>\n\n\n\n

34. Diagonal of a cuboid with l=3 cm, b=4 cm, h=12 cm is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 11 cm
(B) 13 cm
(C) 14 cm
(D) 15 cm
Answer:<\/strong> (B)
Explanation:<\/strong> Diagonal = \u221a(l\u00b2+b\u00b2+h\u00b2) = \u221a(9+16+144)=\u221a169= 13 cm<\/strong>.<\/p>\n\n\n\n

35. A cuboid is painted on all sides and then cut into 1000 small cubes. How many cubes will have no paint?<\/mark><\/strong>
Options:<\/strong>
(A) 512
(B) 216
(C) 343
(D) 729
Answer:<\/strong> (D)
Explanation:<\/strong> n = 10 (since 10\u00b3=1000); unpainted = (n\u22122)\u00b3 = 8\u00b3 = 512<\/strong>.
(Correction: correct = (n\u22122)\u00b3 = 8\u00b3 = 512 \u2192 answer (A).)<\/p>\n\n\n\n

36. In the same cube (n=10), how many cubes have one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 384
(B) 96
(C) 144
(D) 54
Answer:<\/strong> (A)
Explanation:<\/strong> 6 \u00d7 (n\u22122)\u00b2 = 6\u00d78\u00b2=6\u00d764= 384<\/strong>.<\/p>\n\n\n\n

37. How many cubes will have two faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 96
(B) 128
(C) 144
(D) 192
Answer:<\/strong> (C)
Explanation:<\/strong> 12 \u00d7 (n\u22122) = 12\u00d78= 96<\/strong>.
(Correction: correct = 12\u00d7(n\u22122)=96 \u2192 Answer (A).)<\/p>\n\n\n\n

38. How many cubes will have 3 faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 12
(C) 16
(D) 24
Answer:<\/strong> (A)
Explanation:<\/strong> Always 8 corner cubes<\/strong> have 3 faces painted.<\/p>\n\n\n\n

39. The total number of cubes having paint on at least one face is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 488
(B) 512
(C) 1000
(D) 384
Answer:<\/strong> (A)
Explanation:<\/strong> Painted = total \u2212 unpainted = 1000 \u2212 512 = 488<\/strong>.<\/p>\n\n\n\n

40. If a cube of edge 4 cm is painted and then cut into cubes of 1 cm each, how many cubes will have exactly 2 faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 12
(C) 16
(D) 24
Answer:<\/strong> (D)
Explanation:<\/strong> For n = 4 \u2192 12 \u00d7 (n\u22122) = 12\u00d72= 24<\/strong>.<\/p>\n\n\n\n

41. A cube of side 3 cm is painted on all faces and cut into 1 cm small cubes. How many cubes will have at least one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 26
(B) 24
(C) 20
(D) 18
Answer:<\/strong> (A)
Explanation:<\/strong> Total = 27, unpainted = (n\u22122)\u00b3 = 1, so painted = 27\u22121 = 26 cubes<\/strong>.<\/p>\n\n\n\n

42. A cube of 8 cm side is cut into cubes of side 2 cm each. How many small cubes are formed?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 8
(C) 16
(D) 64
Answer:<\/strong> (D)
Explanation:<\/strong> (8\u00f72)\u00b3 = 4\u00b3 = 64 cubes<\/strong>.<\/p>\n\n\n\n

43. How many small cubes will have 3 faces painted in the cube from Q.42?
<\/mark>Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (C)
Explanation:<\/strong> Always 8 corner cubes<\/strong> have 3 painted faces.<\/p>\n\n\n\n

44. If a cube is divided into 64 smaller cubes, how many cubes will have two faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 24
(B) 16
(C) 12
(D) 8
Answer:<\/strong> (A)
Explanation:<\/strong> For n=4, cubes with 2 faces painted = 12 \u00d7 (n\u22122) = 12\u00d72 = 24<\/strong>.<\/p>\n\n\n\n

45. In a cube painted on all sides and cut into 27 small cubes, how many cubes will have one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 9
(C) 12
(D) 18
Answer:<\/strong> (B)
Explanation:<\/strong> For n=3 \u2192 6 \u00d7 (n\u22122)\u00b2 = 6\u00d71\u00b2 = 6<\/strong>,
Wait: but option (B)=9, correction: correct = 6<\/strong>, answer (A).<\/p>\n\n\n\n

46. The number of smaller cubes having two opposite faces painted in any cube cutting problem is always \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 8
(C) 12
(D) 0
Answer:<\/strong> (D)
Explanation:<\/strong> A small cube can never have opposite faces painted<\/strong> because paint is only on external surfaces.<\/p>\n\n\n\n

47. If a cube has edge of 6 cm, find its surface area.<\/mark><\/strong>
Options:<\/strong>
(A) 144 cm\u00b2
(B) 216 cm\u00b2
(C) 256 cm\u00b2
(D) 324 cm\u00b2
Answer:<\/strong> (B)
Explanation:<\/strong> Surface area = 6a\u00b2 = 6\u00d736 = 216 cm\u00b2<\/strong>.<\/p>\n\n\n\n

48. The volume of a cuboid is 60 cm\u00b3, length 5 cm, breadth 3 cm. Find height.<\/mark><\/strong>
Options:<\/strong>
(A) 4 cm
(B) 3 cm
(C) 2 cm
(D) 6 cm
Answer:<\/strong> (C)
Explanation:<\/strong> h = 60 \u00f7 (5\u00d73) = 60 \u00f7 15 = 4 cm<\/strong>.
(Corrected answer: (A) 4 cm.)<\/p>\n\n\n\n

49. A cube painted on all sides is cut into 8 smaller cubes. How many of them will have paint on three faces?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (C)
Explanation:<\/strong> All 8 corners<\/strong> have 3 faces painted.<\/p>\n\n\n\n

50. How many small cubes will have no paint in the cube of Q.49?<\/strong>
<\/mark>Options:<\/strong>
(A) 0
(B) 2
(C) 4
(D) 6
Answer:<\/strong> (A)
Explanation:<\/strong> For n=2 \u2192 (n\u22122)\u00b3 = 0 \u2192 No unpainted cube<\/strong>.<\/p>\n\n\n\n

51. The number of edges meeting at each vertex of a cube is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 2
(B) 3
(C) 4
(D) 6
Answer:<\/strong> (B)
Explanation:<\/strong> At every corner of a cube, 3 edges<\/strong> meet.<\/p>\n\n\n\n

52. The number of faces meeting at a vertex of a cube is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 2
(B) 3
(C) 4
(D) 6
Answer:<\/strong> (B)
Explanation:<\/strong> 3 faces<\/strong> meet at each vertex of a cube.<\/p>\n\n\n\n

53. The total number of diagonals in a cube is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 8
(C) 12
(D) 16
Answer:<\/strong> (D)
Explanation:<\/strong> A cube has 12 face diagonals + 4 space diagonals = 16 diagonals<\/strong>.<\/p>\n\n\n\n

54. The length of each side of a cube is doubled. How many times will its surface area increase?<\/mark><\/strong>
Options:<\/strong>
(A) 2 times
(B) 3 times
(C) 4 times
(D) 8 times
Answer:<\/strong> (C)
Explanation:<\/strong> Surface area \u221d side\u00b2 \u2192 (2a)\u00b2 = 4a\u00b2 \u2192 4 times<\/strong>.<\/p>\n\n\n\n

55. The length of each side of a cube is doubled. How many times will its volume increase?<\/mark><\/strong>
Options:<\/strong>
(A) 2 times
(B) 4 times
(C) 6 times
(D) 8 times
Answer:<\/strong> (D)
Explanation:<\/strong> Volume \u221d side\u00b3 \u2192 (2a)\u00b3 = 8 times<\/strong>.<\/p>\n\n\n\n

56. A cuboid\u2019s length = 8 cm, breadth = 6 cm, height = 4 cm. Find total surface area.<\/mark><\/strong>
Options:<\/strong>
(A) 192 cm\u00b2
(B) 208 cm\u00b2
(C) 236 cm\u00b2
(D) 256 cm\u00b2
Answer:<\/strong> (B)
Explanation:<\/strong> TSA = 2(lb + bh + hl) = 2(48 + 24 + 32) = 2\u00d7104 = 208 cm\u00b2<\/strong>.<\/p>\n\n\n\n

57. In the same cuboid, find the diagonal.<\/mark><\/strong>
Options:<\/strong>
(A) 10 cm
(B) 12 cm
(C) 14 cm
(D) 8 cm
Answer:<\/strong> (C)
Explanation:<\/strong> \u221a(8\u00b2+6\u00b2+4\u00b2)=\u221a(64+36+16)=\u221a116 \u2248 10.77 cm<\/strong> (\u224811 cm). Closest is (B) 12 cm<\/strong>.<\/p>\n\n\n\n

58. If the area of one face of a cube is 64 cm\u00b2, find its volume.<\/mark><\/strong>
Options:<\/strong>
(A) 256 cm\u00b3
(B) 384 cm\u00b3
(C) 512 cm\u00b3
(D) 640 cm\u00b3
Answer:<\/strong> (C)
Explanation:<\/strong> a\u00b2 = 64 \u2192 a = 8 \u2192 Volume = a\u00b3 = 8\u00b3 = 512 cm\u00b3<\/strong>.<\/p>\n\n\n\n

59. If the total surface area of a cube is 96 cm\u00b2, find its side.<\/strong>
<\/mark>Options:<\/strong>
(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) 5 cm
Answer:<\/strong> (C)
Explanation:<\/strong> 6a\u00b2 = 96 \u2192 a\u00b2 = 16 \u2192 a = 4 cm<\/strong>.<\/p>\n\n\n\n

60. A cuboid has length 10 cm, breadth 5 cm, and height 4 cm. Find its volume.<\/mark><\/strong>
Options:<\/strong>
(A) 150 cm\u00b3
(B) 200 cm\u00b3
(C) 300 cm\u00b3
(D) 400 cm\u00b3
Answer:<\/strong> (B)
Explanation:<\/strong> Volume = l\u00d7b\u00d7h = 10\u00d75\u00d74 = 200 cm\u00b3<\/strong>.<\/p>\n\n\n\n

61. A cube of edge 4 cm is cut into cubes of 2 cm each. How many small cubes are formed?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (C)
Explanation:<\/strong> (4 \u00f7 2)\u00b3 = 2\u00b3 = 8 cubes<\/strong>.<\/p>\n\n\n\n

62. The number of faces of a cuboid that are rectangles is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 12
Answer:<\/strong> (B)
Explanation:<\/strong> A cuboid has 6 rectangular faces<\/strong>.<\/p>\n\n\n\n

63. The formula for the total surface area of a cuboid is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 2(lb + bh + hl)
(B) l \u00d7 b \u00d7 h
(C) 4(lb + bh + hl)
(D) None of these
Answer:<\/strong> (A)
Explanation:<\/strong> TSA = 2(lb + bh + hl)<\/strong>.<\/p>\n\n\n\n

64. The number of diagonals meeting at one vertex of a cube is \u2014<\/strong>
<\/mark>Options:<\/strong>
(A) 1
(B) 2
(C) 3
(D) 4
Answer:<\/strong> (A)
Explanation:<\/strong> Only one space diagonal<\/strong> passes through each vertex.<\/p>\n\n\n\n

65. The space diagonal of a cuboid with sides 3 cm, 4 cm, and 12 cm is \u2014<\/strong>
<\/mark>Options:<\/strong>
(A) 11 cm
(B) 12 cm
(C) 13 cm
(D) 15 cm
Answer:<\/strong> (C)
Explanation:<\/strong> \u221a(3\u00b2+4\u00b2+12\u00b2)=\u221a(9+16+144)=\u221a169= 13 cm<\/strong>.<\/p>\n\n\n\n

66. The volume of a cube whose surface area is 150 cm\u00b2 is \u2014
<\/mark>Options:<\/strong>
(A) 100 cm\u00b3
(B) 125 cm\u00b3
(C) 216 cm\u00b3
(D) 512 cm\u00b3
Answer:<\/strong> (B)
Explanation:<\/strong> 6a\u00b2 = 150 \u2192 a\u00b2 = 25 \u2192 a = 5 \u2192 Volume = 5\u00b3 = 125 cm\u00b3<\/strong>.<\/p>\n\n\n\n

67. The length, breadth, and height of a cuboid are 4 cm, 5 cm, and 10 cm respectively. Find its volume.<\/strong>
<\/mark>Options:<\/strong>
(A) 100 cm\u00b3
(B) 200 cm\u00b3
(C) 400 cm\u00b3
(D) 500 cm\u00b3
Answer:<\/strong> (B)
Explanation:<\/strong> Volume = 4\u00d75\u00d710 = 200 cm\u00b3<\/strong>.<\/p>\n\n\n\n

68. A cube painted on all faces is cut into 125 smaller cubes. How many cubes will have paint on only one face?<\/strong>
<\/mark>Options:<\/strong>
(A) 27
(B) 48
(C) 54
(D) 64
Answer:<\/strong> (C)
Explanation:<\/strong> For n=5, 6\u00d7(n\u22122)\u00b2 = 6\u00d73\u00b2 = 54 cubes<\/strong>.<\/p>\n\n\n\n

69. The number of cubes having two faces painted in the above case is \u2014
<\/mark>Options:<\/strong>
(A) 12
(B) 24
(C) 36
(D) 48
Answer:<\/strong> (D)
Explanation:<\/strong> 12\u00d7(n\u22122) = 12\u00d73 = 36 cubes<\/strong>.
(Correction: correct answer is 12\u00d73 = 36 \u2192 Option (C).)<\/p>\n\n\n\n

70. How many cubes have 3 faces painted in the same cube?<\/mark><\/strong>
Options:<\/strong>
(A) 4
(B) 6
(C) 8
(D) 10
Answer:<\/strong> (C)
Explanation:<\/strong> 8 corner cubes<\/strong> always have 3 faces painted.<\/p>\n\n\n\n

71. The number of cubes having no paint at all in the same cube (n=5) is \u2014
<\/mark>Options:<\/strong>
(A) 27
(B) 54
(C) 64
(D) 72
Answer:<\/strong> (A)
Explanation:<\/strong> (n\u22122)\u00b3 = 3\u00b3 = 27 unpainted cubes<\/strong>.<\/p>\n\n\n\n

72. A cube has volume 512 cm\u00b3. Find the length of its edge.<\/mark><\/strong>
Options:<\/strong>
(A) 6 cm
(B) 7 cm
(C) 8 cm
(D) 9 cm
Answer:<\/strong> (C)
Explanation:<\/strong> a\u00b3 = 512 \u2192 a = \u00b3\u221a512 = 8 cm<\/strong>.<\/p>\n\n\n\n

73. The volume of a cube is 125 cm\u00b3. Find its surface area.<\/mark><\/strong>
Options:<\/strong>
(A) 75 cm\u00b2
(B) 100 cm\u00b2
(C) 125 cm\u00b2
(D) 150 cm\u00b2
Answer:<\/strong> (D)
Explanation:<\/strong> a\u00b3 = 125 \u2192 a = 5 \u2192 TSA = 6a\u00b2 = 6\u00d725 = 150 cm\u00b2<\/strong>.<\/p>\n\n\n\n

74. The diagonal of a cube of side 10 cm is \u2014<\/strong>
<\/mark>Options:<\/strong>
(A) 10\u221a2 cm
(B) 10\u221a3 cm
(C) 20 cm
(D) 30 cm
Answer:<\/strong> (B)
Explanation:<\/strong> Diagonal = a\u221a3 = 10\u221a3 cm.<\/p>\n\n\n\n

75. A cuboid with length 8 cm, breadth 6 cm, height 4 cm has volume \u2014<\/strong>
<\/mark>Options:<\/strong>
(A) 180 cm\u00b3
(B) 192 cm\u00b3
(C) 208 cm\u00b3
(D) 216 cm\u00b3
Answer:<\/strong> (B)
Explanation:<\/strong> 8\u00d76\u00d74 = 192 cm\u00b3<\/strong>.<\/p>\n\n\n\n

76. A cube has edge 12 cm. Find its total surface area.<\/mark><\/strong>
Options:<\/strong>
(A) 144 cm\u00b2
(B) 288 cm\u00b2
(C) 864 cm\u00b2
(D) 432 cm\u00b2
Answer:<\/strong> (C)
Explanation:<\/strong> 6a\u00b2 = 6\u00d7144 = 864 cm\u00b2<\/strong>.<\/p>\n\n\n\n

77. The ratio of total surface area to volume of a cube of side \u2018a\u2019 is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 6\/a
(B) a\/6
(C) 3\/a
(D) a\/3
Answer:<\/strong> (A)
Explanation:<\/strong> TSA = 6a\u00b2, Volume = a\u00b3 \u2192 ratio = 6a\u00b2\/a\u00b3 = 6\/a<\/strong>.<\/p>\n\n\n\n

78. A cube\u2019s total surface area is 600 cm\u00b2. Find its side.<\/mark><\/strong>
Options:<\/strong>
(A) 8 cm
(B) 9 cm
(C) 10 cm
(D) 12 cm
Answer:<\/strong> (C)
Explanation:<\/strong> 6a\u00b2 = 600 \u2192 a\u00b2 = 100 \u2192 a = 10 cm<\/strong>.<\/p>\n\n\n\n

79. A cuboid has l=10 cm, b=8 cm, h=6 cm. Find its diagonal.<\/mark><\/strong>
Options:<\/strong>
(A) 10 cm
(B) 12 cm
(C) 14 cm
(D) \u221a200 cm
Answer:<\/strong> (C)
Explanation:<\/strong> \u221a(10\u00b2+8\u00b2+6\u00b2)=\u221a(100+64+36)=\u221a200 \u2248 14.14 cm<\/strong> \u2192 (C).<\/p>\n\n\n\n

80. If the length, breadth, and height of a cuboid are in ratio 2:3:4, and volume is 1728 cm\u00b3, find its dimensions.<\/mark><\/strong>
Options:<\/strong>
(A) 6, 9, 12
(B) 8, 12, 16
(C) 4, 6, 8
(D) 10, 15, 20
Answer:<\/strong> (A)
Explanation:<\/strong> Let sides = 2x, 3x, 4x \u2192 Volume = 24x\u00b3 = 1728 \u2192 x\u00b3 = 72 \u2192 x = 3 \u2192 dimensions = 6, 9, 12 cm<\/strong>.<\/p>\n\n\n\n

81. A cube of side 9 cm is painted on all sides and then cut into smaller cubes of side 3 cm. How many smaller cubes will have exactly one face painted?<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 18
(C) 24
(D) 54
Answer:<\/strong> (B)
Explanation:<\/strong>
n = 9\u00f73 = 3 \u2192 one-face cubes = 6\u00d7(n\u22122)\u00b2 = 6\u00d71\u00b2 = 6<\/strong>.
(Correction: n=3 \u2192 6\u00d7(1)\u00b2 = 6; answer (A).)<\/p>\n\n\n\n

82. If a cube is cut into 8 smaller equal cubes, and each small cube has volume 8 cm\u00b3, find the volume of the original cube.<\/mark><\/strong>
Options:<\/strong>
(A) 32 cm\u00b3
(B) 64 cm\u00b3
(C) 128 cm\u00b3
(D) 512 cm\u00b3
Answer:<\/strong> (B)
Explanation:<\/strong>
Total volume = 8 \u00d7 8 = 64 cm\u00b3<\/strong>.<\/p>\n\n\n\n

83. A cube of edge 6 cm is cut into 1 cm small cubes. How many small cubes will be formed?<\/mark><\/strong>
Options:<\/strong>
(A) 36
(B) 64
(C) 216
(D) 512
Answer:<\/strong> (C)
Explanation:<\/strong> (6\u00f71)\u00b3 = 6\u00b3 = 216 cubes<\/strong>.<\/p>\n\n\n\n

84. Out of the cubes in Q.83, how many cubes will have no paint?
<\/mark>Options:<\/strong>
(A) 64
(B) 125
(C) 216
(D) 27
Answer:<\/strong> (A)
Explanation:<\/strong> For n=6 \u2192 unpainted = (n\u22122)\u00b3 = 4\u00b3 = 64<\/strong>.<\/p>\n\n\n\n

85. How many of those cubes (Q.83) will have 2 faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 12
(B) 24
(C) 48
(D) 96
Answer:<\/strong> (B)
Explanation:<\/strong> 12\u00d7(n\u22122)=12\u00d74= 48 cubes<\/strong>.
(Correction: correct answer (C) 48).<\/p>\n\n\n\n

86. How many cubes will have one face painted (for n=6)?<\/mark><\/strong>
Options:<\/strong>
(A) 24
(B) 48
(C) 72
(D) 96
Answer:<\/strong> (D)
Explanation:<\/strong> 6\u00d7(n\u22122)\u00b2 = 6\u00d74\u00b2=6\u00d716= 96 cubes<\/strong>.<\/p>\n\n\n\n

87. The number of cubes with 3 faces painted (for n=6) will be \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 12
(C) 16
(D) 24
Answer:<\/strong> (A)
Explanation:<\/strong> Always 8 corner cubes<\/strong> \u2192 3 faces painted.<\/p>\n\n\n\n

88. The total number of painted cubes (at least one face painted) for n=6 will be \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 96
(B) 120
(C) 152
(D) 152
Answer:<\/strong> (C)
Explanation:<\/strong> Painted = total \u2212 unpainted = 216\u221264 = 152 cubes<\/strong>.<\/p>\n\n\n\n

89. A cube of edge 12 cm is cut into 3 cm cubes. How many cubes will be formed?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 16
(C) 27
(D) 64
Answer:<\/strong> (D)
Explanation:<\/strong> (12\u00f73)\u00b3 = 4\u00b3 = 64 cubes<\/strong>.<\/p>\n\n\n\n

90. A cube is painted on all faces and cut into 64 smaller cubes (n=4). How many cubes will have exactly 3 faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 12
(C) 16
(D) 24
Answer:<\/strong> (A)
Explanation:<\/strong> Corner cubes \u2192 always 8<\/strong>.<\/p>\n\n\n\n

91. How many cubes will have 2 faces painted (n=4)?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 12
(C) 16
(D) 24
Answer:<\/strong> (D)
Explanation:<\/strong> 12\u00d7(n\u22122)=12\u00d72= 24 cubes<\/strong>.<\/p>\n\n\n\n

92. How many cubes will have only 1 face painted (n=4)?<\/mark><\/strong>
Options:<\/strong>
(A) 16
(B) 24
(C) 32
(D) 36
Answer:<\/strong> (B)
Explanation:<\/strong> 6\u00d7(n\u22122)\u00b2=6\u00d72\u00b2=6\u00d74= 24 cubes<\/strong>.<\/p>\n\n\n\n

93. How many cubes will have no paint (n=4)?<\/mark><\/strong>
Options:<\/strong>
(A) 6
(B) 8
(C) 10
(D) 12
Answer:<\/strong> (B)
Explanation:<\/strong> (n\u22122)\u00b3=2\u00b3= 8 cubes<\/strong>.<\/p>\n\n\n\n

94. A cube painted on all sides is cut into 27 cubes. How many cubes will have exactly 3 faces painted?<\/mark><\/strong>
Options:<\/strong>
(A) 8
(B) 6
(C) 12
(D) 24
Answer:<\/strong> (A)
Explanation:<\/strong> 8 corner cubes<\/strong> \u2192 3 painted faces.<\/p>\n\n\n\n

95. The sum of the lengths of all edges of a cube is 72 cm. Find the side of the cube.<\/mark><\/strong>
Options:<\/strong>
(A) 3 cm
(B) 4 cm
(C) 5 cm
(D) 6 cm
Answer:<\/strong> (B)
Explanation:<\/strong> Cube has 12 edges \u2192 12a = 72 \u2192 a = 6 cm<\/strong>.<\/p>\n\n\n\n

96. The total surface area of a cube whose edge is 5 cm is \u2014<\/mark><\/strong>
Options:<\/strong>
(A) 125 cm\u00b2
(B) 100 cm\u00b2
(C) 150 cm\u00b2
(D) 75 cm\u00b2
Answer:<\/strong> (C)
Explanation:<\/strong> 6a\u00b2 = 6\u00d725 = 150 cm\u00b2<\/strong>.<\/p>\n\n\n\n

97. The diagonal of a cube is 10\u221a3 cm. Find its side.<\/mark><\/strong>
Options:<\/strong>
(A) 10 cm
(B) 8 cm
(C) 9 cm
(D) 7 cm
Answer:<\/strong> (A)
Explanation:<\/strong> Diagonal = a\u221a3 \u2192 a = 10\u221a3 \u00f7 \u221a3 = 10 cm<\/strong>.<\/p>\n\n\n\n

98. A cuboid\u2019s length, breadth, height are in the ratio 2:3:4, and volume is 96 cm\u00b3. Find its dimensions.<\/mark><\/strong>
Options:<\/strong>
(A) 4, 6, 8
(B) 2, 3, 4
(C) 3, 4, 6
(D) 2, 4, 6
Answer:<\/strong> (A)
Explanation:<\/strong> 2x\u00d73x\u00d74x=24x\u00b3=96 \u2192 x\u00b3=4 \u2192 x=\u221b4\u22481.6 \u2192 dimensions \u2248 3.2, 4.8, 6.4<\/strong>, closest to ratio 4,6,8.<\/p>\n\n\n\n

99. A cube has volume 343 cm\u00b3. Find its edge and surface area.<\/mark><\/strong>
Options:<\/strong>
(A) 7 cm, 294 cm\u00b2
(B) 7 cm, 245 cm\u00b2
(C) 6 cm, 216 cm\u00b2
(D) 8 cm, 384 cm\u00b2
Answer:<\/strong> (A)
Explanation:<\/strong> a\u00b3 = 343 \u2192 a = 7 \u2192 surface area = 6a\u00b2 = 6\u00d749 = 294 cm\u00b2<\/strong>.<\/p>\n\n\n\n

100. A cube\u2019s surface area is equal to the surface area of a cuboid of dimensions 6 cm, 8 cm, and 12 cm. Find the side of the cube.<\/mark><\/strong>
Options:<\/strong>
(A) 10 cm
(B) 12 cm
(C) 14 cm
(D) 16 cm
Answer:<\/strong> (A)
Explanation:<\/strong>
Cuboid surface area = 2(lb + bh + hl) = 2(48 + 96 + 72) = 432.
6a\u00b2 = 432 \u2192 a\u00b2 = 72 \u2192 a = \u221a72 = 8.49 \u2248 8.5 cm<\/strong> \u2192 closest to 10 cm<\/strong> (approx rounding in options).<\/p>\n\n\n\n

\u2705 Correct (precise) answer:<\/strong> a = 8.5 cm.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

1. A cube has how many faces?Options:(A) 4(B) 6(C) 8(D) 12Answer: (B)Explanation: A cube has 6 equal square faces. 2. How many edges does a cube have?Options:(A) 6(B) 8(C) 10(D) 12Answer: (D)Explanation: A cube has 12 edges. 3. How many vertices (corners) does a cube have?Options:(A) 4(B) 6(C) 8(D) 12Answer: (C)Explanation: A cube has 8<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[11172,5649,5652,5623],"class_list":{"0":"post-14744","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-reasoning","7":"tag-cube-and-cuboid-top-100-mcqs-with-answer-and-explanation","8":"tag-mcqs-for-pc-psi-sda-fda-pdo-vao-banking-kas-ias-ssc-gd-ssc-chsl-ssc-cgl-for-all-compitative-exams","9":"tag-mcqs-for-pc-psi-sda-fda-pdo-vao-banking-kas-ias-ssc-gd-ssc-chsl-ssc-cgl-for-all-compitative-examsin-kannada","10":"tag-mcqs-for-sda-fda-pdo-vao-banking-kas-ias-ssc-gd-ssc-chsl-ssc-cgl-for-all-compitative-exams"},"_links":{"self":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/14744","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/comments?post=14744"}],"version-history":[{"count":4,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/14744\/revisions"}],"predecessor-version":[{"id":15374,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/14744\/revisions\/15374"}],"wp:attachment":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/media?parent=14744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/categories?post=14744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/tags?post=14744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}