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Answer :

Given, the sides of the cuboid as 5 cm, 2 cm and 5 cm.

So we have the volume of the cuboid =\( 5 cm \times 2 cm \times 5 cm = 50 cm^3\)

We have the prime factors of 50 as:

\(50 = 2 \times 5 \times 5\)

To make it a perfect cube, we must have \(2 \times 2 \times 2 \times 5 \times 5 \times 5\)

\(\Rightarrow 20 \times (2 \times 5 \times 5)\)

\(\Rightarrow 20 \times volume \;of \;the\; given \;cuboid\)

Thus,we have the required number of cuboids = 20.

- 1.Which of the following numbers are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656
- 2.Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100
- 3.Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. (i) 81 (ii) 128 (iii) 135 (iv) 92 (v) 704

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