Question

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

• A. 12 m, 8 m, 4 m
• B. 36 m, 24 m, 12m
• C. 9 m, 6 m, 3 m
• D. 39 m, 26 m, 13 m

Answer 1

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

$\therefore$ Volume of the block of stone
$=3x\times 2x\times x=6x^3{m}^3$
But it is given that volume of the stone = 10368 $m^3$
$⟹x^3=\frac{10368}{6}=1728$
$⟹x=\sqrt[3]{31728}=(12\times 12\times 12{)}^{\frac{1}{3}}=({12}^3{)}^{\frac{1}{3}}=12m$

Hence, the length of the stone = 3 $\times$ 12 = 36 m
Breadth of the stone = 2 $\times$ 12 = 24 m
Height of the stone = 1 $\times$12 = 12 m