Question

If a cylinder with height 9 inches and radius 4 inches is filled with water, it can fill a certain pitcher. How many of these pitchers can a cylinder with the same height and a radius twice as large fill.

Answer 1

We will need 4 pitchers to fill with water the new cylinder.

Explanation:

The volume of the first cylinder is:

`V_(1)=\pi r^(2)h` (1)

Where:

• r is the radius
• h is the height

Using the values of the problem we have:

`V_(1)=\pi 4^(2)9`

`V_(1)=452.4\: in^(3)`

We know that it can fill a certain pitcher, so the volume of the pitcher is 452.4 in³.

Let's find the new volume of the second cylinder to find how many of these pitchers can this cylinder.

We know that the cylinder has the same height and the radius is 2 times the older one.

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

`V_(2)=\pi (2*4)^(2)9`

`V_(2)=1809.6\: in^(3)`

Now, we just need to divide V(2) by V(1) to find the number of pitchers (np).

`np=(1809.6)/(452.4)=4`

Therefore, we will need 4 pitchers to fill with water the new cylinder.

I hope it helps you!