The radius of the circle has increased by 25%. How much percent will the area of the circle increase?
July 25, 2021 | education|
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%.
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