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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.

It is impossible to get four varnished faces out of a big cube. Hence answer is zero.

Tiny cubes having only two faces varnished = (x - 2) × number of edges = (6 - 2) × 12 = 4 × 12 = 48. Hence option D is the answer.

Tiny cubes having only two faces varnished = (x - 2) × number of edges = (4 - 2) × 12 = 2 × 12 = 24. Hence option C is the correct answer.

Q 4 - Sanghamoyra has a cube which has length of 9 cm, breadth of 5 cm, and height of 2 cm and is segmented into tiny cubes. How many such tiny cubes can be formed?

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

= 9 × 5 × 2 = 90.

Q 5 - What will be length of the portion of tiny cubes, if each portion of the original big cube is 4 cm and the cube is segmented into 125 tiny ones?

Number of tiny cubes = 125. Cube root of 125 = 5. So x = 5 cm. 5 = (4/portion of tiny cube) or portion of tiny cube = 4/5 = 0.8 cm.

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 - A big cube whose all the corners are named as M, N, O, P, Q, R, S and T. Its each portion is of 54 cm in length. The cube is segmented into tiny cubes and length of the portion of each tiny cube is 6 cm. How many such cubes are possible?

To find the number of tiny cubes first we have to find x. So x = (54/6) = 9. So number of tiny cubes M = 9 × 9 × 9 = 729. Hence option B is the answer.

Q 8 - A big cube whose each corner is named as G, H, J, K, L, M, N and P is having each portion of 72 cm. This cube is segmented into tiny cubes of portion 9 cm each. All the faces of the original big cube is varnished pink before being cut.

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

Here x = 72/9 = 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) x number of faces = (8 - 2) × (8 - 2) × 6 = 6 × 6 × 6 = 216. Hence option C is the answer.

Q 9 - A big cube is segmented into tiny cubes and each portion of the tiny cubes is of equal length. The total number of tiny cubes formed is 343. Each portion of the tiny cubes is 2 cm. Find out the length of each portion of the original bigger cube.

Total number of tiny cubes = 343. Cube root of 343 is 7. So x = 7. By formula, portion of big cube = 7 × 2 = 14. Hence option C is correct.

Q 10 - A big cube is having 80 cm portion and the tiny cubes cut out of it is having 8 cm each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?

Here x = 80/8 = 10. Such cubes can be found by following method. X – 2 = 10 - 2 = 8. So 8 × 8 × 8 = 512. So number of cubes will be formed such that each face of these cubes is surrounded by other cubes is 512.

reasoning_cube_and_cuboid.htm

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