Question

The volume of a rectangular block of stone is 10368 m3. If its length, breadth and height are in the ratio 3 : 2 : 1, then its length, breadth and height are

- 12 m, 8 m, 4 m
- 36 m, 24 m, 12m
- 39 m, 26 m, 13 m
- 9 m, 6 m, 3 m

Solution

The correct option is **B** 36 m, 24 m, 12m

Given, length : breadth : height = 3 : 2 : 1

Let the height of block =x m

Then, length of block =3x m

breadth of block =2x m

∴ Volume of the block of stone

=3x×2x×x=6x3 m3

But it is given that volume of the stone = 10368 m3

⟹ x3=103686=1728

⟹ x=3√1728 =(12×12×12)13 =(123)13 =12 m

Hence, the length of the stone = 3 × 12 = 36 m

Breadth of the stone = 2 × 12 = 24 m

Height of the stone = 1 ×12 = 12 m

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