A conical cup is 4 cm across and 8 cm deep.

Question

A conical cup is  across and  deep. Water leaks out of the bottom at the rate of  What is the rate of change of the water's level when the height of the water is ?

Answer 1

Radius, r = Diameter/2 = 4/2 = 2

dV/dt = -3 cm³/m

By similar triangles, r/h = 2/8 --> r = h/4

V=(1/3)πr²h = (1/3)πh³/16 = πh³/48

dV/dt = (3/48)πh²dh/dt = (1/16)πh²dh/dt

dh/dt = 16dV/dt/(πh²)

When h = 4

dh/dt = 16(-3)/16π = -3/π cm/m

So the water level is dropping at 3/π cm/m