Question

Water is being pumped into an inverted right circular conical tank at the rate 30 ft^3/min. the tank, which stands vertex down and base up, has a height of 12 ft and a base diameter of 16 ft. how fast is the water level rising when the water is 9 ft deep?

Answer 1

at depth h, h = 3/2 r

v = 1/3 pi r^2 h
v = 1/3 pi r^2 (3r/2)
v = pi/2 r^3

dv/dt = 3pi/2 r^2 dr/dt

30 = 3pi/2 * 36 dr/dt
dr/dt = 5/(9pi)

Answer 2

thanks steve