How much does the area of the original circle increase?

Question

A circle has a radius of A meters. If the radius doubles,how much does the area of the original circle increase?

Answer 1

area of a circle

area = π r^2

let radius = A and if we double the radius then r = 2A

therefore

area = π(2A)^2

area = π(4A)

so if the radius doubles then the area increases by a factor of 4