Question

The volume of a rectangular block of stone is 10368 $d{m}^3$. If its length, breadth, and height are in the ratio 3 : 2 : 1, then its length, breadth, and height are

• A. 36 dm, 18 dm, 4 dm
• B. 36 dm, 24 dm, 12 dm
• C. 18 dm, 14 dm, 36 dm
• D. 36 dm, 18 m, 21 dm

Answer 1

The correct option is B

36 dm, 24 dm, 12 dm

Let the length of block = 3x dm
Breadth of block = 2x dm
Height of block = x dm
$\therefore$ Volume of the block of stone
$3x\times 2x\times x=6x^{3}d{m}^3$
But the given volume of the stone = 10368 $d{m}^3$
$\therefore x^3=\frac{10368}{6}=1728$
$\Rightarrow x=\sqrt[3]{31728}=(12\times 12\times 12{)}^{\frac{1}{3}}=({12}^3{)}^{\frac{1}{3}}=12$
Hence, the length of the stone = 3 $\times$ 12 = 36 dm
Breadth of the stone = 2 $\times$ 12 = 24 dm
Height of the stone = 1 $\times$12 = 12 dm