Answer: \(30\pi\text{ cm}^2\text{ s}^{-1}\).

The area of the circle is

\(A=\pi r^2.\)

Differentiate with respect to \(r\):

\(\frac{dA}{dr}=2\pi r.\)

The radius is increasing at

\(\frac{dr}{dt}=5.\)

Using the chain rule,

\(\frac{dA}{dt}=\frac{dA}{dr}\cdot\frac{dr}{dt}.\)

So

\(\frac{dA}{dt}=2\pi r\cdot5=10\pi r.\)

When \(r=3\),

\(\frac{dA}{dt}=10\pi(3)=30\pi.\)

The area is increasing at

\(30\pi\text{ cm}^2\text{ s}^{-1}.\)