Math derivative calcular relative rates

Question

A large snowball is melting so that it's radius is decreasing at the rate of 2 inches per hour. How fast is the volume decreasing at the moment that the radius is 3inches? HINT: volume of a sphere is V=4/3(pi)r³

 

The answer I got is dr/dt =2/4(pi)(9) ... can anyone tell me where I keep going wrong/ show the correct way??

 

Thanks a ton!

Marina

Answer 1

dV/dt = 4(pi)r²(dr/dt)

 

Given: dr/dt = -2; r = 3

Find: dV/dt

 

when r = 3 inches dV/dt = 4(pi)(3²)(-2) = -72pi sq in/hour