Question

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the

Answer 1

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?

Answer:

`(1)/(\pi)$ m/s`

Explanation:

Volume of a cylinder,
`V=\pi r^2h`

When the water is leaking, the radius of the cylinder remains constant while the height changes with respect to time.

Therefore, the rate of change of the volume,

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

`4=\pi * 2^2 * (dh)/(dt)\\\\(dh)/(dt)=(4)/(4\pi)\\\\(dh)/(dt)=(1)/(\pi)$ m/s`