Question

Water is being poured into a cylindrical vase at a rate of 15 millilitres per second. If the radius of the vase is 10 cm, find the rate with which the height of water in the vase is rising. ?

Answer 1

The height of water in the vase is rising at 0.0478cm/second

Explanation:

Lets first find the volume of the vase at 1cm.
`V=pir^2*h`
`V=pi(10)^2*1`
`V=100picm^3`
`V=100pi ml`

So, the vase hold 100`pi` for 1cm of height.
As the water is flowing in at 15ml/second, we can now determine how long it takes the water to fill 1cm (height wise) of the vase and therefore the rate at which it rises.

`15/(100pi)=0.0478`cm/second