SOLUTION: Air is let out of a spherical balloon at a rate of 300 cm^3 s^-1. Find the rate at which the radius is decreasing when a) the radius is 2 cm, b) the volume is 367pi cm^3

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Question 1191912: Air is let out of a spherical balloon at a rate of 300 cm^3 s^-1. Find the rate at which the radius is
decreasing when
a) the radius is 2 cm,
b) the volume is 367pi cm^3
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Air is let out of a spherical balloon at a rate of 300 cm^3 s^-1.
dV%2Fdt+=+-300cm%2Fs

So we want a formula for the volume of a sphere:

V=expr%284%2F3%29pi%2Ar%5E3
dV%2Fdt=3%2Aexpr%284%2F3%29pi%2Ar%5E2%2Aexpr%28dr%2Fdt%29
Substitute -300 for dV%2Fdt and simplify
-300=4pi%2Ar%5E2%2Aexpr%28dr%2Fdt%29
-75=pi%2Ar%5E2%2Aexpr%28dr%2Fdt%29

Find the rate at which the radius is
decreasing when
a) the radius is 2 cm,
Substitute 2 for r in the last equation and solve 
for dr%2Fdt

b) the volume is 367pi cm^3
 

Substitute 367pi for V in V=expr%284%2F3%29pi%2Ar%5E3, 

Solve for r

Substitute that value for r in

-75=pi%2Ar%5E2%2Aexpr%28dr%2Fdt%29

Solve for dr%2Fdt



Edwin