# Thread: Rate of Change of the volumee of a sphere

1. ## Rate of Change of the volumee of a sphere

What is the rate of change of the area of a sphere with respect to the radius when the radius is r=3?

I have a vague idea.
They want us to use (f(t+h)-f(t))/h.

Guess: Plug in t as $pi r^2$ as t ans solve. Then plug 2 in for r.

Thanks!

2. Take the derivative of the formula for the surface area of a sphere and plug 3 in for r once you've taken the derivative.

Post if you need more clarification.

3. Originally Posted by Truthbetold
What is the rate of change of the area of a sphere with respect to the radius when the radius is r=3?

I have a vague idea.
They want us to use (f(t+h)-f(t))/h.

Guess: Plug in t as $pi r^2$ as t ans solve. Then plug 2 in for r.

Thanks!
no. first thing, what is the function we are using here?

find the function for the area, then use it as f(r) in the formula above. and replace r with 3, because that's what the question says.

so you want: $\lim_{h \to 0}\frac {f(3 + h) - f(3)}h$

recall, the formula for the area of a sphere is $A = 4 \pi r^2$

4. Sorry, I forgot to specify to use the formula. Make sure you're using that if they specify to use it.