Question

The area of three adjacent faces of a cuboid are $X,Y,$ and $Z$, respectively, then the volume of the cuboid is:

• A. $XYZ$
• B. $3XYZ$
• C. $\sqrt{XYZ}$
• D. $\sqrt{3XYZ}$

Answer 1

The correct option is C $\sqrt{XYZ}$

Let the length breadth and height of the cuboid be $l,b,h$ Units respectively.

Now Area of the adjacent face of the cuboid are $X,YandZ$ respectively.

Area of face ABCD$=x\times h=X........\left(1\right)$

Area of face ACGF$=b\times h=Y........\left(2\right)$

Area of face ABEF$=l\times b=Z.........\left(3\right)$

Multiplying equation (1) (2) and (3) we get

$XYZ=l^2{b}^2{h}^2$

$l^2{b}^2{h}^2=XYZ\left(lbh\right)=\sqrt{XYZ}$

Where $lbh$ is volume of the cuboid.

$V=\sqrt{XYZ}$