Question

A paper cup is the shape of a cone with a height of 12 cm and radius 4 cm at the top. Water is poured into he cup at a rate of 2cm^3/s. How fast is the water level rising when the water level is 8 cm deep?

Answer 1

V = pi r^2 h / 3
dV = (pi/3)*(2rdr + r^2 * dh)
since h/12 = r/4 r =h/3 and dr =dh/3
dV/dt =(pi/3)*(2(h/3)((dh/dt)/3) + (h/3)^2 * dh/dt)
dV/dt = 2 and h = 8
2 =(pi/3)*(2(8/3)((dh/dt)/3) + (8/3)^2 * dh/dt)
solve for dh/dt

Answer 2

maybe I'm working it out wrong but the sheet says that I should get 9/32pi for the answer and instead I'm getting 27/56pi