Question

A box with a square base of side a is three times higher than it is wide. Express the volume V of the box as a function of a.
V(a) = ?

Answer 1

volume of a box is length x width x height.

Here its bottom is square, with side= a (its side has length a)
The box is three times higher. This means 3 times a is its height.
So putting it together:
length= a, width =a (square base)
height= 3a (three times higher than it is wide)
\[V=a\cdot a\cdot 3a=3a^3\]