Water flowing into a hemispherical tank of 5m radius at a rate of ((3m^3)/(hr))

Question

Determine the rate at which the depth of water increases.

Answer 1

The volume of a spherical cap of height y on a sphere of radius 5 is

v = 1/3 pi y^2 (15-y)
dv/dt = pi y(10-y) dy/dt
3 = pi y(10-y) dy/dt

Since you haven't specified depth of the water when determining the measurement, this is as far as we can go for now.