Question

18. If a cylinder with height 4 inches and radius r is filled with water, it can fill a certain pitcher. How many of these pitchers can a cylinder with height 4 inches and radius 3r fill?​

Answer 1

9 pitchers

Explanation:

we know that

The volume of a cylinder is equal to

`\text{V}=\pi r^2h`

Step 1

Find the volume of the cylinder with height 4 inches and radius r

substitute the given values

`\text{V}_1=\pi r^2(4)`

`\text{V}_1=4\pi r^2 \ in^3`

Step 2

Find the volume of the cylinder with height 4 inches and radius 3r

substitute the given values

`\text{V}_2=\pi(3r)^2(4)`

`\text{V}_2=36\pi r^2 \ in^3`

Step 3

we know that

The volume of the cylinder 1 can fill a certain pitcher,

so

The volume of the pitcher is the same that the volume of cylinder 1

therefore

the number of pitchers that can be filled by the second cylinder is equal to divide the volume of the second cylinder by the volume of the first cylinder

`(36\pi r^2 )/(4\pi r^2) =9 \ \text{pitchers}`