The radius of the circle has increased by 25%. How much percent will the area of the circle increase?

The area of a circle is calculated by the formula S = пR ^ 2.

The radius has increased by 25%. The radius was 100%, now 100% + 25% = 125%.

Let’s convert percentages to decimal numbers: 125%: 100% = 1.25.

This means that the area of the new circle will be calculated by the formula S1 = п (1.25R) ^ 2.

Let’s simplify the expression: P (1.25R) ^ 2 = п * 1.5626R ^ 2 = 1.5626 * пR ^ 2.

Since the area of the original circle is S = пR ^ 2, the area of the new circle is 1.5626 part of the area of the original one, that is, it will increase by 0.5625 part.

Let’s translate 0.5625 into percent: 0.5625 * 100% = 56.25%.

Answer: the area will increase by 56.25%.