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?
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%.