Question

The surface area of $3$ coterminous faces of cuboid are $6c{m}^2$, $15c{m}^2$ and $20c{m}^2$ respectively. The volume of cuboid is:

• A. $30\sqrt{2}c{m}^3$
• B. $40c{m}^3$
• C. $20c{m}^3$
• D. $35c{m}^3$

Answer 1

The correct option is A $30\sqrt{2}c{m}^3$

Let length, breadth and height of cuboid be $l,bandh$ respectively. Now

$lb=6,bh=15,hl=20$

$\Rightarrow lb.bh.hl=6\times 15\times 20\Rightarrow {\left(lbh\right)}^2=1800$

$\Rightarrow lbh=\sqrt{1800}=30\sqrt{2}$

Therefore Volume of cuboid $=$ $30\sqrt{2}{cm}^3$