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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.

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

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.

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 - What will be length of the portion of tiny cubes, if each portion of the original big cube is 14 cm and the cube is segmented into 343 tiny ones?

Here number of tiny cubes = 343. Cube root of 343 = 7. So x = 7 cm.

2 = (14/portion of tiny cube) or portion of tiny cube = 14/7 = 2 cm.

Q 5 - A big cube whose all the corners are named as A, B, C, D, E, F, G and H. Its each portion is of 20 cm length. The cube is segmented into tiny cubes and length of the portion of each tiny cube is 4 cm. Then how many such cubes are possible?

To find the number of tiny cubes, first we have to find x. So x = (20/4) = 5. So number of tiny cubes = 5 × 5 × 5 = 125. Hence option C.

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 A, B, C, D, E, F, G and H. Its each portion is of 60 cm in length. The cube is segmented into tiny cubes and length of the portion of each tiny cube is 3 cm. How many such cubes are possible?

To find the number of tiny cubes first we have to find x. So x = (60/3) = 20. So number of tiny cubes = 20 × 20 × 20 = 8000. Hence option C is the answer.

Q 8 - Koushik has a cube which has length of 6 cm, breadth of 5 cm and height of 3 cm and is segmented into tiny cubes. How many such tiny cubes can be formed?

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

= 6 × 5 × 3 = 90.

Q 9 - 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 is 512. Each portion of the tiny cubes is 4 cm. Find out the length of each portion of the original bigger cube.

Total number of cubes = 512. Cube root of 512 is 8. So x = 8. By formula, portion of big cube = 8 × 4 = 32. Hence option A is correct.

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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