SOLUTION: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1 in^3/min. How fast is its radius shrinking when it is 3 inches? Answer must be in in^

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Question 1082911: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1 in^3/min. How fast is its radius shrinking when it is 3 inches? Answer must be in in^3/min.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the surface area of a sphere,
A=4pi%2AR%5E2
Differentiate with respect to time,
dA%2Fdt=%284pi%292R%2A%28dR%2Fdt%29
Substituting,
1=%284pi%29%282%283%29%29%28dR%2Fdt%29
dR%2Fdt=1%2F%2824pi%29in%2Fs
The units of the change of radius are inches per second.
The volume change is in units of cubic inches/second.