if a cylinder with height 9 inches and radius r 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 fill? explain how you know.

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

[tex]\frac{36\pi r^{2}}{9\pi r^{2}}=4\ pitchers[/tex]

psm22415 psm22415 · Answer 2 · 2022-01-10T14:25:36+01:00

There are 4 pitchers can a cylinder with a height of 9 inches and radius 2r fill and it can be determined by using formula of cylinder.

Given that,

If a cylinder with a height of 9 inches and radius r is filled with water, it can fill a certain pitcher.

We have to determine,

How many of these pitchers can a cylinder with a height of 9 inches and radius of 2r fill?

According to the question,

Let n be number of pitchers cylinder,

If a cylinder with a height of 9 inches and radius r is filled with water.

Then,

The volume of the cylinder is given by,

[tex]\rm v = \pi r^2h\\\\v = \pi r^2(9)\\\\v = 9\pi r^2[/tex]

And these pitchers can a cylinder with a height of 9 inches and radius of 2r fill,

Then,

The volume of the cylinder is given by,

[tex]\rm v = \pi r^2h\\\\v = \pi (2r)^2(9)\\\\v = 36\pi r^2[/tex]

Therefore,

The number of pitchers can a cylinder with a height of 9 inches and radius of 2r fill is determined by the ratio of the volume of the second cylinder and first cylinder.

[tex]\rm n = \dfrac{Volume \ of \ second \ cylinder}{Volume \ of \ first \ cylinder}\\\\n = \dfrac{36\pi r^2}{9\pi r^2}\\\\n = \dfrac{4}{1}\\\\n = 4[/tex]

Hence, 4 pitchers can a cylinder with a height of 9 inches and radius 2r fill.

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