If the radius of a circle is increased by 15%, its area increases by ____.

The area of a circle is given by the formula:
A=πr
2

When the radius r is increased by 15%, the new radius becomes r
′
=1.15r.

The new area A
′
is:

A
′
=π(1.15r)
2
=1.3225πr
2
=1.3225A
The percentage increase in the area can be calculated using the successive percentage increase formula:

Percentage Increase=x+y+
100
xy
​

Since both dimensions increase by 15%, we substitute x=15 and y=15:

Percentage Increase=15+15+
100
15×15
​

Percentage Increase=30+
100
225
​
=30+2.25=32.25%