Answer
The area of the garden increases by a percentage of 56%.
Work Step by Step
The original area of the garden is $A_0 = \pi r_0^2$
The original radius $r_0$ increases by 25%, so the new radius $r$ is $1.25 ~r_0$
We can find the ratio of new area $A$ of the garden to the original area $A_0$.
$ratio = \frac{A}{A_0} = \frac{\pi r^2}{\pi r_0^2} = \frac{\pi (1.25~r_0)^2}{\pi r_0^2} = \frac{(1.25)^2~r_0^2}{ r_0^2} = (1.25)^2 = 1.56$
The area of the garden increases by a factor of 1.56 which is an increase of 56%.
