# A snowball, in the shape of a sphere, is melting so that the radius is decreasing at a uniform rate of 1cm/s. How fast is the volume decreasing when the radius equals 6cm?

##### 2 Answers

We can write the first relationship (in

We know that the formula for the volume of a sphere is:

Also, the derivative of

Thus, if we differentiate this with respect to

Finally, we can plug it in:

Therefore, when

The volume is decreasing at a rate of

#### Explanation:

We are told that

We need to find

We know:

So:

So when the radius