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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 33 cm portion and the tiny cubes cut out of it is having 11 cm in each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?

Here x = 33/11 = 3. Such cubes can be found by following method. X – 2 = 3 - 2 = 1 and 1 × 1 × 1 = 1. So, number of cubes will be formed such that each face of these cubes is surrounded by other cubes is only one.

Tiny cubes having only two faces varnished = (x - 2) × number of edges = (10 - 2) × 12 = 8 × 12 = 96. Hence option D is the answer.

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

Q 4 - What will be length of the portion of tiny cubes, if each portion of original big cube is 10 cm and the cube is segmented into 125 tiny cubes?

Number of tiny cubes = 125. Cube root of 125 = 5. So x = 5 cm.

5 = (10/portion of tiny cube) or portion of tiny cube = 10/5 = 2 cm.

Q 5 - A big cube is segmented into tiny cubes and each portion of the tiny cubes are of equal length. The total number of tiny cubes formed are 27. Each portion of the tiny cube is 3 cm. Then find out the length of each portion of the original bigger cube.

Number of cube = 27. Cube root of 27 is 3. So x= 3. By formula, portion of big cube = 3 × 3 = 9. Hence option B is correct.

Q 6 - A big cube whose all the corners are named as H, I, J, K, L, M, N and O. Its each portion is of 35 cm length. The cube is segmented into tiny cubes and length of the portion of each tiny cube is 5 cm. How many such cubes are possible?

To find the number of tiny cubes first we have to find x. So x = (35/5) = 7. So number of tiny cubes = 7 × 7 × 7 = 343. Hence option A is the correct answer.

Q 7 - Harry has a cube whose each portion is of 15 cm. If she wants to cut tiny cubes of portion 1.5 cm each, then how many such cubes will be possible for her?

x = (15/1.5) = 10

So total number of cubes = 10 × 10 × 10 = 1000. Hence option C is correct.

Tiny cubes having only two faces varnished = (x - 2) × number of edges = (8 - 2) × 12 = 6 × 12 = 72. Hence option D is the option.

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 8. Each portion of the tiny cubes is 1 cm. Find out the length of each portion of the original bigger cube.

Total number of tiny cubes is = 8. Cube root of 8 is 2. So x = 2. By formula portion of big cube = 2 × 1 = 2. Hence option D is correct.

Q 10 - A cube is segmented into 512 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 512 = 8. 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 = (8 - 2) × 12 = 72. Total number of cubes whose three faces are varnished are the number of corners = 8. So total number of required cubes = 72 + 8 = 80. Hence option D is the answer.

reasoning_cube_and_cuboid.htm

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