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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.

Q 2 - A big cube whose each corner is named as A, B, C, D, E, F, G and H is having each portion 30 cm. This cube is segmented into tiny cubes of portion 5 cm each. All the faces of the original big cube is varnished with white colour before being cut.

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

Here x = 30/5 = 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 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 the original big cube is 8 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 = (8/ portion of tiny cube) or portion of tiny cube = 8/5 = 1.6 cm.

x = 6. So x - 2 = 6 - 2 = 4. 4 × 4 × 4 = 64.

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 length of the portion of tiny cubes, if the original big cube having each portion of 40 cm is segmented into 125 tiny ones?

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

5 = (40/ portion of tiny cube) or portion of tiny cube = 40/5 = 8 cm.

Q 8 - A big cube whose each corner is named as E, F, G, H, I, J, K and L is having each portion 45 cm. This cube is segmented into tiny cubes of portion 5 cm each. All the faces of the original big cube is varnished velvet before being cut.

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

Here x = 45/5 = 9. So number of tiny cubes can be formed is M = 9 × 9 × 9 = 729.

Cubes having only one face varnished is = (x - 2) x (x - 2) x number of faces = (9 - 2) × (9 - 2) × 6 = 7 × 7 × 6 = 294. Hence option D is the answer.

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

Q 10 - A big cube is having 64 cm 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 = 64/8 = 8 cm. So x - 2 = 8 - 2 = 6. Finally 6 × 6 × 6 = 216. Hence answer is option A.

reasoning_cube_and_cuboid.htm

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