# Homework Help: Implicit differentiation and related rates

1. Nov 4, 2013

### Panphobia

1. The problem statement, all variables and given/known data

The spherical head of a snowperson is melting under the HOT sun at the rate of -160 cc/h (cubic centimetres per hour.) Find the rate at which the radius is changing when the radius r=16. Use cm/h for the units.
(The volume of a sphere is given by V= 4π⋅r^3/3.)

I have missed the past few calculus lectures and I am afraid I am falling behind, how would I start this kind of question? I know that the volume is changing at a rate of V - 160t where t is the number of hours...but I don't know how that helps at all.

2. Nov 4, 2013

### Tanya Sharma

V = (4/3)πr3

Differentiate both sides with respect to ‘t’ .What do you get ?

3. Nov 4, 2013

### Panphobia

dV/dt = 4πr^2*dr/dt

4. Nov 4, 2013

### Tanya Sharma

Excellent...

Now,dV/dt and 'r' is given to you .Just calculate dr/dt .

5. Nov 4, 2013

### Panphobia

Oh my (facepalm) thank you so much for the help!

6. Nov 4, 2013

### Tanya Sharma

:thumbs:

You are welcome

7. Nov 4, 2013

### Panphobia

If I was to do the same thing but instead I was given a volume and was looking for the rate of change of volume given the rate of change of radius, would I just isolate for r then take the derivative?

8. Nov 5, 2013

### Tanya Sharma

That would be quite tedious .

Instead, from the given volume just find out the radius using the relation V =(4/3)πr3 .Then approach in the similar manner .