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.

Step-by-step explanation:

The question is not displaying correctly. Part c is unclear.

r, V, and h are the radius, volume, and height, respectively.

V = πr²h

Since h = 9 in, V = 9πr² in³

a. See picture.

b. The relationship between r and V is not linear. The volume increases exponentially as r increases linearly.

c. Let R be the radius of the larger cylinder.

Volume of larger cylinder = 9πR²

Volume of pitcher = 9πr²

(9πR²)/(9πr²) = R²/r²

The larger cylinder can fille R²/r² pitchers.

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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for