# 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. ?

Aug 6, 2017

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

#### Explanation:

Lets first find the volume of the vase at 1cm.
$V = \pi {r}^{2} \cdot h$
$V = \pi {\left(10\right)}^{2} \cdot 1$
$V = 100 \pi c {m}^{3}$
$V = 100 \pi m l$

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.

$\frac{15}{100 \pi} = 0.0478$cm/second