Question

Help! *MEDAL*

Answer 1

A circle is growing so that each side is increasing at the rate of 3 cm/min. How fast is the area of the circle changing at the instant the radius is 12 cm? Include units in your answer.

Answer 2

@mathmale @zepdrix

Answer 3

each side .... of a circle...?

Answer 4

Exactly.

Answer 5

I guess teacher probably meant to say "the radius is increasing at this rate"

Answer 6

So let's get our area formula, ya?\[\large\rm A=\pi r^2\]And we're going to take a derivative, with respect to time.

Answer 7

ok...

Answer 8

a little confused.

Answer 9

They want us to figure out the instantaneous rate of change of the area, when r=12.
\(\large\rm A'(12)=?\)
That's what we're trying to figure out.

Answer 10

144pi

Answer 11

It'll be a little tricky, cause we need to apply chain rule.\[\large\rm A=\pi r^2\]So we'll power rule, into chain rule.\[\large\rm A'=2\pi r\cdot r'\]

Answer 12

No you calculated A(12).
We want A'(12)

Answer 13

so 2pi(12)

Answer 14

The radius is increasing at a rate of 3cm/min.
This is our r' variable. The instantaneous rate of change of the radius r.
\(\large\rm r'=3\)
And they want us to evaluate this at \(\large\rm r=12\)

So we need to plug all of those goodies in.

Answer 15

Right. 2pi(12)(3) ?...

Answer 16

72 pi or 226.2

Answer 17

@zepdrix ??

Answer 18

Oh sorry ran off for a min >.<
Yah that seems about right.\[\large\rm 72 \pi\]Do you understand what the units are?

Answer 19

cm./min?

Answer 20

good :)

Answer 21

so the answer would be 72pi cm/min

Answer 22

If you'd please show your work (all of it), I'd be glad to give you feedback on it.