posted by Mark .
A spherical balloon is being inflated in such a way that its radius increases at a rate of 3 cm/min. If the volume of the balloon is 0 at time 0, at what rate is the volume increasing after 5 minutes?
my answer is 45 cm/min.
is this right. thanks
First, volume is cm^3
v = 4/3 pi r^3
dv/dt = 4 pi r^2 dr/dt
at t=5, r=15 so
dv/dt = 4 pi * 225 * 3 = 2700 pi cm^3/min
How did you come up with 45? Way small, and I'd surely expect a pi to appear somewhere in any problem involving a sphere.
My fault lied in plugging in directly. Thank you for showing me the steps.