Question

A cylindrical tank has a radius of 20 cm. Water flows out of the tank at .05 liters per second. How fast does the level of water in the tank drop?

Answer 1

Explanation:

To calculate the rate at which the water level drops, we need to find the volume of water being lost per second and convert that to a height change. The volume of water being lost is given as 0.05 liters per second. The volume of a cylinder with height h and radius r is given by the formula:

V = πr^2h

We can rearrange this formula to solve for h:

h = V / (πr^2)

Substituting the given values, we get:

h = 0.05 / (π * 20^2) = 0.05 / (π * 400) = 0.05 / 1257.0796

So the rate at which the water level is dropping is approximately 0.04 cm per second.