There are many cylinders with a height of 9 inches. Let LaTeX: rr represent the radius in inches and LaTeX: VV represents the volume in cubic inches.

a. Complete the table relating the radius and volume of cylinders with height 9 inches. Write each volume as a multiple of LaTeX: \piπ or round to the nearest cubic inch.

b. Is there a linear relationship between the radius and the volume of these cylinders? Explain how you know.

c. If a cylinder with height 9 inches and radius LaTeX: rr is filled with water, it can fill a certain pitcher. How many of these pitchers can a cylinder with height 9 inches and radius LaTeX: 2r2 r fill? Explain how you know.

The answers to all the parts is given below.

The formula to calculate the compound interest is -

[tex]$A =P(1 + \frac{r}{n}) ^{nt}[/tex]

Given are many cylinders with a height of 9 inches.

{ 1 } -

We can complete the table as -

{r}  :           1                     2                     3

V{c} :   π x (1)² x 9      π x (2)² x 9      π x (3)² x 9

{V} :         9π                  36π                 81π

{ 2 } -

For the linear relationship -

{36π - 9π}/{2 - 1} = {81π - 36π}/{3 - 2}

27π ≠ 45π

It is not a linear relationship

{ 3 } -

Volume of pitcher = π x (r)² x 9 = 9πr²

Volume of cylinder with radius 2r = π x (2r)² x 9 = 9π x 4r² = 36πr²

The cylinder can fill -

n = 36πr²/9πr²

n = 4 pitchers

Therefore, the answers to all the parts is given above.

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