Question

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

• A. 20 cubic cm
• B. 30 cubic cm
• C. 35 cubic cm
• D. 40 cubic cm

Answer 1

The correct option is B 30 cubic cm

Let the three adjacent faces be $A_1,A_2,A_3$

where $A_1=6c{m}^2,A_2=15c{m}^2$ and $A_3=10c{m}^2$

Then volume of the cuboid is given be $V=\sqrt{A_1{A}_2{A}_3}$

$=\sqrt{6\times 15\times 10}$

$=\sqrt{900}$

$=30c{m}^3$