Question

when a cylindrical tank is filled with water at a rate of 3 cubic meters per minute what does dh/dt equal

Answer 1

`(dh)/(dt)=(3)/(\pi r^(2))` meters per minute

Explanation:

Volume of a cylinder is given by the formula,

V = πr²h

Where r = radius of the cylindrical tank

h = height of the tank

Water is filling in this tank = 3 cubic meters per second

Derivative of volume will show the change in volume of the water in the tank.

`(dV)/(dt)=(d)/(dt)(\pi r^(2)h)`

`(dV)/(dt)=(\pi r^(2)) (dh)/(dt)`

By putting
`(dV)/(dt)=3` in the expression,

`3=(\pi r^(2)) (dh)/(dt)` [Since 'r' is a constant]

`(dh)/(dt)=(3)/(\pi r^(2))`

Therefore, rate of increase in height of the water level will be represented by,

`(dh)/(dt)=(3)/(\pi r^(2))` meters per minute