SOLUTION: Air is blown into a Spherical balloon and the rate at which the volume is increasing is 3 ft^3 per minute. Find the rate at which the radius is increasing at the instant when the r

Algebra ->  Bodies-in-space -> SOLUTION: Air is blown into a Spherical balloon and the rate at which the volume is increasing is 3 ft^3 per minute. Find the rate at which the radius is increasing at the instant when the r      Log On


   

Question 1170380: Air is blown into a Spherical balloon and the rate at which the volume is increasing is 3 ft^3 per minute. Find the rate at which the radius is increasing at the instant when the radius is 5 feet.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the equation for the volume of a sphere:
+V+=+%284%2F3%29pi%2Ar%5E3+

you can relate the rate of change of volume WRT time (dV/dt) to the product (dV/dr)*(dr/dt):
+dV%2Fdt+=+%28dV%2Fdr%29%2A%28dr%2Fdt%29+=+4pi%2Ar%5E2+%2A+%28dr%2Fdt%29+ ... (1)

Plugging into (1) the known values:
+3+=+4pi%285%29%5E2+%2A+%28dr%2Fdt%29+

and solving for dr/dt:
+dr%2Fdt+=+0.00955+ ft/min