Question

The volume of a cylinder of fixed height varies in direct proportion to the square of the base radius. How do you find the change in volume when the base radius is increased by 18%?

Answer 1

Volume increases by `39.24%`

Explanation:

As the volume of a cylinder, say `V`, of fixed height varies in direct proportion to the square of the base radius, say `r`, we can write the relation as

`Vpropr^2` and as `r` is increased by `18%`

i.e. it increases from `r` to `118/100r` or `1.18r`,

Volume will increase by `(1.18r)^2=1.3924r^2`

and hence volume increases by `39.24%`