Question

If 'l', 'b', and 'h' are the length, breadth, and height of the rectangular box respectively, then the product of the areas of all the faces of the box is equal to

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

Answer 1

The correct option is D

square of the volume

A rectangular box is a cuboid.
'l', 'b', and 'h' are the length, breadth, and height of the rectangular box respectively.
Bottom area = lb
Side area = bh
Front area = lh
The product of the areas of all the faces of the box is
$=lb\times bh\times lh=l^2{b}^2{h}^2=(lbh{)}^2=(volume{)}^2$
[$\because$ volume of cuboid = lbh]