Question

The volume of a spherical balloon of radius r cm is V cm3, where .
Find dv/dr
My answer: 4πr^2

The balloon leaks at 5cm^3 per second, how fast does the radius of the balloon leaks when the radius is 15 cm.
Find the rate at which the radius is changing with time when the volume is 680 cm^3.

Answer 1

yes, dV/dr = 4 pi r^2 which is in fact the surface area (note, the surface area * dr = change in volume for small dr)



You already know that dV/dr = 4 pi r^2
so calculate dV/dr
then
dV/dt = dV/dr * dr/dt
-5 = dV/dr * dr/dt
so calculate dr/dt from that

part 2
(4/3) pi r^3 = 680
so calculate new r and dr/dt