Question

Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm.

Answer 1

You know the volume of a sphere can be expressed as\[V=\frac{4}{3}\pi r^3.\]We're told that\[\frac{dV}{dt}=5,\]and we're asked to find\[\frac{dr}{dt}\]whenever \(r=10\).

Perform implicit differentiation:\[\frac{dV}{dt}=4\pi r^2\frac{dr}{dt},\]\[5=400\pi\frac{dr}{dt},\]\[\frac{dr}{dt}=\frac{1}{80\pi}.\]The units are cm/min.

Answer 2

thank you =)