Question

The radius of a circle is 9cm. By what amount must the radius be increased to increase the area
by 19π square centimeters? (HINT: Recall that the area of a circle is A = πr2
.)

Answer 1

\[A=\pi r^2\]
The radius is 9, so you have
\[A=9^2\pi=81\pi\]
You want area to increase by 19π, so you want to solve for x in this equation:
\[81\pi+19\pi=81\pi+(9+x)^2\pi\\
(81\pi+19\pi=\text{Previous area $+$ new area})\]

Answer 2

Thank you! :)