We know that `A=pi r^2,` and in this case the radius and thus the area are functions of `t,` so we use the chain rule and differentiate both sides *with respect to `t.` *The result is

`(dA)/(dt)=2pi r (dr)/(dt).`

Substituting `r=1` and `(dr)/(dt)=3` in the right side, we get

`(dA)/(dt)=2pi(1)(3)=6pi`` `,

**so the area is changing at the rate of** `6pi` **at the instant** ` ``r=1`.

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now