A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 5 feet per minute. Find the rate at which the area is changing at the instant the radius is 17 feet.

Question

anonymous · Answer

$$
A=\pi r^2
$$

anonymous · Answer

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

anonymous · Answer

How about at 7ft radius?

anonymous · Answer

" The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 5 feet per minute."

This means $dr/dt=5$

anonymous · Answer

"the radius is 17 feet"

$r=17$

anonymous · Answer

"Find the rate at which the area is changing"

Find $dA/dt$

anonymous · Answer

$$
\frac{dA}{dt}=(2\pi r)\frac{dr}{dt}=2\pi (17)(5)
$$

anonymous · Answer

@Sarah1362894 Use the algebra.  Let go.

anonymous · Answer

I try and I'm wrong everytime

anonymous · Answer

The answer is $170\pi$ isn't it?

anonymous · Answer

Nope just tried it

anonymous · Answer

did you put in the unit of ft squared per minute?