Question

The radius r of a circle is increasing at a rate of 6 centimeters per minute.
a. Find the rate of change of the area when r = 10 centimeters.
b. Find the rate of change of the area when r = 28 centimeters.

Answer 1

The answers should be in cm^2/min.

Answer 2

OK - you want to use calculus?

Answer 3

yes

Answer 4

so write the equation for area of a circle

Answer 5

this is calculus using derivatives right?

Answer 6

yes

Answer 7

so write the equation for area of a circle

Answer 8

I think its area=r^2Pi

Answer 9

correct

so what is dA/dr

( the derivative)

Answer 10

\[\frac{ dA }{ dt }=\frac{ d }{ dt }\left[ r^2 \pi \right]\]

Answer 11

right?

Answer 12

but im not sure how to do Product rule for r^2 pi

Answer 13

You will actually get da/dt = pi(2r * dr/dt). This is using both the chain rule and power rule

Answer 14

What Batman is saying is that r is a function of t as well so we require to do chain rule

Answer 15

yes. very much so.

Answer 16

Any further question?

Answer 17

A good way too look at this and how to solve it is this video:

https://www.youtube.com/watch?v=KFMHUuCnOsU&list=PLsJ7E_UWMp2wTSq8C0wpJVuwQWbSaqHxZ

Answer 18

so do I just plug in the radius?

Answer 19

Batman pretty much did all, you just need to plug in the values

Answer 20

you have to insert two values. you need to plug in dr/dt and the r. We know what both values are.

Answer 21

notice dr/dt =6

Answer 22

da/dt=pi(2(10cm)*(dr/dt)
so what is dr/dt ?

Answer 23

ok now it makes sense :)

Answer 24

Ok good:)

Answer 25

Remember what dr/dt actually is. its a slope, or a rate of change. :)

Answer 26

I'm actually working on a similiar problem right now. haha

Answer 27

THanks i was thinking about what would be dr/dt. Thank you all!

Answer 28

thanks @BATMAN*