Question

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

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

Answer 1

The correct option is A

$30c{m}^3$

Cuboid

A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.

It is given that, the areas of coterminous faces of a cuboid as $6,15,10$ $c{m}^2$ :

• $l\times b=6c{m}^2$
• $l\times h=15c{m}^2$
• $b\times h=10c{m}^2$

The formula for volume of a cuboid is $\mathit{l}\mathbf{}\mathbf{\times }\mathbf{}\mathit{b}\mathbf{}\mathbf{\times }\mathbf{}\mathit{h}\mathbf{}$

multiply above three equations, we get

$(l\times b)\times (l\times h)\times (b\times h)=6\times 15\times 10$

$\Rightarrow l^2\times b^2\times h^2=6\times 15\times 10$

$\Rightarrow {(l\times b\times h)}^2=900$

$\Rightarrow {(l\times b\times h)}^{}=\sqrt{900}$

$\Rightarrow l\times b\times h=30$

Therefore, the formula for cuboid is, $l\times b\times h=30$$c{m}^3$

Hence, the correct option is A