# Thread: The rate at which the volume of a sphere changes

1. ## The rate at which the volume of a sphere changes

Find the rate at which the volume of a sphere is changing with respect to its radius.
$\displaystyle V = (4/3)pi*r$

Any help is appreciated. Thanks.

2. Originally Posted by lancelot854
Find the rate at which the volume of a sphere is changing with respect to its radius.
$\displaystyle V = (4/3)pi*r$

Any help is appreciated. Thanks.
You need to take the derivative with respect to r

Note your formula for the volume of a sphere is incorrect

$\displaystyle \displaystyle V=\frac{4}{3} \pi r^3$

3. Oh, I must of written the formula down wrong. xD

Does this first step look correct?

$\displaystyle \frac{dv}{dx} = \frac{4}{3} \pi 3r^2 \frac{dr}{dx}$

4. Originally Posted by lancelot854
Oh, I must of written the formula down wrong. xD

Does this first step look correct?

$\displaystyle \frac{dv}{dx} = \frac{4}{3} \pi 3r^2 \frac{dr}{dx}$
where did the variable $\displaystyle x$ come from ? the problem statement says to take the derivative w/respect to the radius ...

$\displaystyle \displaystyle \frac{dV}{dr} = 4\pi r^2$

you're done.