# 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?

22.5%

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 $$A = {\pi}(\frac{d}{2}) ^{2}$$
So, if the diameter of the logo increases by 45%, the radius increases by $$\frac{{45}}{2} = 22.5\%$$ which, in turn, increases the total area by 22.5%.