Related Rates Problem

Question

A spherical balloon currently has a radius of 16 inches. If the radius is still growing at a rate of 3 inches per second, at what rate is air being pumped into the balloon?

Round answer to nearest hundredth.

Step by step explanation. Not on a video.

Answer 1

r=16 in (now), growing at a rate of 3 in => dr/dt=3 in/sec

at what rate is air being pumped into the balloon? => dV/dt = ?

V=4/3 *r^3*pi

dV/dt = 4r^2*pi *dr/dt

at r=16 in

dV/dt=4*16^2*pi*3 = 3072 pi in^3/sec = 9650.972632 in^3/sec