Question

A cylinder has a radius of 3 cm and a height of 25 cm. We fill the cylinder with water to a height of 15 cm. Then we add 5 golf balls to the water. Each golf ball has a radius of 2.2 cm. What will the new height of the water be?

Answer 1

The new height of the water will:

`H_(new)=22.89 cm`

Explanation:

The submerged volume due to an object in a liquid, water in our case, is equal to the displaced volume of the water, it is the Archimedes principle.

The volume of a golf ball (sphere) will be

`V_(ball)=(4)/(3)\pi r^(3)=(4)/(3)\pi 2.2^(3)`

`V_(ball)=44.6 cm^(3)`

We have 5 golf balls, so the total volume will be:

`V_(5-ball)=5*44.6 cm^(3)=223\: cm^(3)`

Using Archimedes' principle the extra volume of water will be 223 cm³

Now, we know that the cylinder has a radius of 3 cm, then the height related to 223 cm³ will be:

`223=\pi r^(2)h`

`223=\pi 3^(2)h`

`h=7.89\: cm`

Therefore, the new height of the water will:

`H_(new)=15+7.89=22.89 cm`

I hope it helps you!