Question

A water tank in the shape of a right circular cylinder has a volume that is increasing at the rate
of 300pi cubic centimeters per hour. If the height is decreasing at the rate of 15 centimeters per hour,
find the rate at which the radius is changing when the radius is 20
centimeters and the height is 30 centimeters.

Answer 1

v = 1/3 pi r^2 h
dv/dt = pi/3 (2rh dr/dt + r^2 dh/dt)
Now just plug in
dv/dt = 300pi
dh/dt = -15
r=20
h=30
and solve for dr/dt