SOLUTION: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1 in 2 /min . How fast is its volume shrinking when its radius is 3 in ?

Question 1172158: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1 in 2 /min . How fast is its volume shrinking when its radius is 3 in ?

Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
the rate of 1 in 2 /min
====================
What does that mean?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Assuming that "1 in 2/min" is supposed to be ...
=
=

V in terms of A:
=

Taking the derivative of V wrt A:
=

Need an expression for dV/dt in terms of information given:
=

At r=3, A= = ---> =

dA/dt is given as

So, finally, = =
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Another approach would be to use 'r' instead of 'A': dV/dt = (dV/dr)*(dr/dt)
It is about equally messy to go this route. Because you are given dA/dt, you
have the additional step dr/dt = (dA/dt)*(dr/dA), so dV/dt = (dV/dr)*(dA/dt)*(dr/dA)
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