Question

calc help

Answer 1

A circle is growing so that each side is increasing at the rate of 2cm/min. How fast is the area of the circle changing at the instant the radius is 10cm? Include units in your answer.

Answer 2

@Zale101

Answer 3

We know that the circle keeps increasing at a rate of 2cm/min. Meaning, the area of a circle keeps increasing.

Answer 4

What is the area of a circle?

Answer 5

pir^2

Answer 6

\(A(r) =\pi r^2\)
How fast is the area of a circle changing? To answer this, we need to take the derivative of the area to obtain the instantaneous value for the rate of change of the area.

Answer 7

2piR(dr/dt)

Answer 8

Your question is asking you to find the area's rate of change.

Answer 9

\(\Large \frac{d(A(r))}{dt}=\frac{dA}{dt}=\frac{d}{dt}[\pi r^2]\)
\(\Large \frac{dA}{dt}=2\pi r \frac{dr}{dt}\)

Answer 10

ok so whats next?

Answer 11

You are giving the radius (r) and dr/dt (the rate of change of the radius). Plug them in the dervative of the area to get dA/dt.

Answer 12

dA/dt= 2pi (10)(2)

Answer 13

Yes.

Answer 14

So the answer is 40pi?

Answer 15

Yes.

Answer 16

ok thanks. i have one more if you don't mind