A spherical snowball is melting

Question

A spherical snowball is melting in such a way that’s it’s radius is decreasing at rate of 0.2 cm/min. At what rate is the volume of the snowball decreeing when the radius is 10cm. (Note the answer is a positive number)

Answer 1

We will use related rates to answer this question. We want to know the relation of the volume to the radius so we can use the equation (this is the volume of a sphere)

V=4/3πr³

We can differentiate this to get the relationship we are looking for

dV/dt=d(4/3πr³)

dV/dt= 4πr² ⋅ dr/dt

Then we can simply plug in

dV/dt = 4π(10)² (-.2)

dV/dt= -80π

However the question is asking for the rate of the ball DECREEING

Our answer tells us the rate is 80π and the negative tells us which way it is going, in this case it is decreeing like we want. So we simply take the numerical answer.

80π

Hope this helps.