# Math Help - Rates of Change - Sphere

1. ## Rates of Change - Sphere

A metal sphere is dissolving in acid. It remains spherical and the rate at which its volume decreases is proportional to its surface area. Show that its radius is decreasing at a constant rate.

2. Here's a kick off

$\displaystyle \frac{dV}{dt}\propto 4\pi r^2$

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

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

Now firstly find $\displaystyle \frac{dV}{dr}$ from $\displaystyle V = \frac{4}{3}\pi r^3$

3. Thanks, the question looked more difficult than it actually is!