# How do you find the rate at which water is pumped into an inverted conical tank that has a height of 6m and a diameter of 4m if water is leaking out at the rate of #10,000(cm)^3/min# and the water level is rising #20 (cm)/min#?

##### 1 Answer

This question has already been answered although you seem to be missing the height of the water in the cone at the time the water level is rising

Assuming this question came from the same source, the specified height of water was

The cone has a radius of 2 m (half the diameter) and a height of 6 m

for a ratio of

This ratio is constant for volumes of water contained in the cone,

Therefore the volume of the cone (or water in the cone), normally written as

can be re-written as

and therefore

We are told

The increase in volume contained in the cone is given by

The inflow of water must be the total of

the outflow (leakage)

plus

the amount needed to raise the water level: