Question

For \[A=\pi r^2\], what is the rate of change of area with respect to radius when \[r=5\] cm?

Options

• \[2\pi\text{ cm}^2/\text{cm}\]

• \[25\pi\text{ cm}^2\]

• \[5\pi\text{ cm}^2/\text{cm}\]

• \[10\pi\text{ cm}^2/\text{cm}\]

Answer 1

First, \[\frac{dA}{dr}=2\pi r\]. Substituting \[r=5\] gives \[2\pi(5)=10\pi\].
The required units are \[\text{cm}^2/\text{cm}\].