Question

The area of three adjacent faces of a cuboid are $6c{m}^2,15c{m}^2$ and $10c{m}^2$. The volume of the cuboid is

• A. $50c{m}^3$
• B. $35c{m}^3$
• C. $40c{m}^3$
• D. $30c{m}^3$

Answer 1

The correct option is D $30c{m}^3$

Let the length, breadth and height of the cuboid be $l,b$ and $h,$ respectively.
Thus, the area of 3 adjacent faces are $lb,bh$ and $hl$.
$\therefore lb=6c{m}^2,bh=15c{m}^2,hl=10c{m}^2$ (Given)
$\therefore \text{Volume of the cuboid = lbh}$
$=\sqrt{(lbh{)}^2}$
$=\sqrt{l^2{b}^2{h}^2}$
$=\sqrt{\left(lb\right)\left(bh\right)\left(hl\right)}$
$=\sqrt{6\times 15\times 10}$
$=\sqrt{900}$
$=30c{m}^3$
Hence, the correct answer is option (d).