Question

The base area, side area and front area of a rectangular box are known. The product of these areas is equal to ___.

• A. the volume of the rectangular box
• B. the square root of the volume of the rectangular box
• C. twice the volume of the rectangular box
• D. the square of the volume of the rectangular box

Answer 1

The correct option is D the square of the volume of the rectangular box

We know that a rectangular box is a cuboid.

Let $l$, $b$ and $h$ be the length, breadth and height of the rectangular box respectively.

Then, base area of the cuboid $=l\times b$
Side area of the cuboid $=b\times h$
Front area of the cuboid $=l\times h$

Now, product of the base, side and front areas of the rectangular box
$=lb\times bh\times lh$
$=l^2{b}^2{h}^2$
$=(lbh{)}^2$

Volume of the rectangular box $=lbh$.

$\therefore$ The product of required areas is equal to the square of the volume of the rectangular box.