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: