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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.

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 class=

Sagot :

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Answer:

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.

View image DWRead
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