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Following quiz provides Multiple Choice Questions (MCQs) related to **Cube and Cuboid**. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using **Show Answer** button. You can use **Next Quiz** button to check new set of questions in the quiz.

Q 1 - A big cube is having 32 cm in each portion. Tiny cubes of 8 cm portion each is cut from that. Then how many tiny cubes will be formed that are surrounded by at least one cube?

Here x = 32/8 = 4 cm. so x - 2 = 4 - 2 = 2. Finally: 2 × 2 × 2 = 8. Hence answer is option A.

The answer is the number of corners available which is 8. Hence option A is the correct answer.

Q 3 - A big cube whose all the corners are named as H, I, J, K, L, M, N and O. Its each portion is of 42 cm length. The cube is segmented into tiny cubes and length of the portion of each tiny cube is 6 cm. Then how many such cubes are possible?

To find the number of tiny cubes, first we have to find x. Here x = (42/6) = 7. So number of tiny cubes M = 7 × 7 × 7 = 343. Hence option A is the answer.

Q 4 - Bhargav has a cube which has length of 10 cm, breadth of 4 cm, and height 2 cm and is segmented into tiny cubes. How many such tiny cubes can be formed?

Number of cubes can be formed = length × breadth × height

= 10 × 4 × 2 = 80.

Q 5 - A big cube whose each corner is named as M, N, O, P, Q, R, S and T is having each portion of 18 cm. This cube is segmented into tiny cubes of portion 3 cm each. All the faces of the original big cube is varnished green before being cut.

How many cubes will be formed having only one face varnished?

Here x = 18/3 = 6. So number of tiny cubes can be formed is M = 6 × 6 × 6 = 216.

Cubes having only one face varnished is = (x - 2) × (x - 2) × number of faces = (6 - 2) × (6 - 2) × 6 = 4 × 4 × 6 = 96. Hence option A is the answer.

Q 6 - A big cube is having 9 cm portion and the tiny cubes cut out of it is having 3 cm for each portion. How many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?

Here x = 9/3 = 3. Such cubes can be found by following method. x – 2 = 3 - 2 = 1. 1 × 1 × 1 = 1. So, number of cubes that will be formed such that each face of these cubes is surrounded by other cubes is only one.

Q 7 - What will be the length of the portion of tiny cubes, if the original big cube having each portion of 36 cm is segmented into 216 tiny ones?

Total number of tiny cubes = 216. Cube root of 216 = 6. So x = 6 cm.

6 = (36/ portion of tiny cube) or portion of tiny cube = 36/6 = 6 cm.

Here x = 9. So x - 2 = 9 - 2 = 7. 7 × 7 × 7 = 343.

Q 9 - A big cube whose each corner is named as C, V, B, N, M, K, H and L is having each portion of 32 cm. This cube is segmented into tiny cubes having portion of 4 cm each. All the faces of the original big cube is varnished navy blue before being cut.

How many cubes will be formed having only one face varnished?

Here x = 32/4 = 8. So number of tiny cubes can be formed is M = 8 × 8 × 8 = 512.

Cubes having only one face varnished is = (x - 2) × (x - 2) × number of faces = (8 - 2) × (8 - 2) × 6 = 6 × 6 × 6 = 216. Hence option C is the answer.

Q 10 - A cube is segmented into 1331 equal tiny cubes. Before dividing the cube, each face of it is varnished in different colours. How many tiny cubes will be formed having more than one colour?

Here x = Cube root of 1331 = 11. More than one colour means two or more colours. So total number of cubes whose two faces are varnished is = (x - 2) × number of edges = (11 - 2) × 12 = 108. The cubes having three faces varnished are the number of corners = 8. So total number of required cubes = 108 + 8 = 116. Hence option C is the answer.

reasoning_cube_and_cuboid.htm

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