Mathematics: Cylinder with height 9 inches and radius is filled with water, it can fill a certain pitcher. How many of these pitchers can a cylinder with height 9 inches and radius 2r r fill?

Cylinder with height 9 inches and radius is filled

dasharia

19.01.2022

Step-by-step explanation:

The 1st cylinder used to fill the pitcher has:

height:

h = 9 in

radius:

r = r

The volume of a cylinder is given by:

$V=\pi r^2 h$

Therefore, the volume of the 1st cylinder is

$V=\pi r^2 9=9\pi r^2$

We are told that the water inside this cylinder can fill a certain pitcher, so this is also the volume of the pitcher.

Then, we have a second cylinder, which has height

h = 9 in

and radius

r' = 2r

So the volume of this cylinder is

$V'=\pi r'^2 h = \pi (2r)^2 9 =9\pi (4r^2)=36\pi r^2$

This means that the number of pitchers that can be filled by this 2nd cylinder is

$n=\frac{V'}{V}=\frac{36\pi r^2}{9\pi r^2}=4$

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