A circular logo is enlarged to fit the lid of a jar. The new diameter is 60% larger than the original. By what percentage has the area of the logo increased?

30%

Explanation

The area of a circle is given by the formula  \( A = {\pi}r^2\) where r is the radius of the circle. The radius of a circle is its diameter divided by two so  \(A = \pi {\left( {\frac{d}{2}} \right)^2}\) So, if the diameter of the logo increases by 60%, the radius increases by \( \frac{{60}}{2} = 30\%\) which, in turn, increases the total area by 30%.

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