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A circular logo is enlarged to fit the lid of a jar. The new diameter is 45% larger than the original. By what percentage has the area of the logo increased?

A. 17.5%

B. 32.5%

C. 22.5%

D. 12.5%


The area of a circle is given by the formula

where r is the radius of the circle. The radius of a circle is its diameter divided by two so

So, if the diameter of the logo increases by 45%, the radius increases by 45/2 = 22.5% which, in turn, increases the total area by 22.5%.

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