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Question

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 12 cm.

Answer 1

The volume of a sphere is:

 

Volume = (4/3)*pi*radius³

 

To find the rate of change of the volume, take the derivative of the Volume wrt time, t.  You will have to use the chain rule to find the derivative.

 

d(Volume)/dt = (8/3)*pi*radius²*d(radius)/dt

 

Now d(radius)/dt = -0.1 cm/min (half of diameter rate) and radius = 6 cm (diameter is 12 cm):

 

d(Volume)dt = (8/3)*pi*6²*(-0.1)

 

Can you finish it from here?