The volume of a cylindrical canister is given by the formula V=nr^2h Part1. Write a function f(V) to express the radius of the canister as a function of the volume. Part 2. Suppose a certain type of canister must have a height of 32 centimeters (cm), so the quantity nh is about 100 cm. Write an updated version of the function f(V), using 100 for nh, to determine the radius of the canister that would result in certain volumes. Complete the table to find the values of f(V) for V = 25; 100; 625; 900; 2,500; and 10,000. Part 3. Plot the points from your table on the grid and sketch the graph. Part 4. If the graph were rotated 90° counterclockwise about the origin, which function would the result resemble? Explain your answers, including relating the two functions
The volume of a cylindrical canister is given by the formula V=nr^2h Part1. Write a function f(V) to express the radius of the canister as a function of the volume. Part 2. Suppose a certain type of canister must have a height of 32 centimeters (cm), so the quantity nh is about 100 cm. Write an updated version of the function f(V), using 100 for nh, to determine the radius of the canister that would result in certain volumes. Complete the table to find the values of f(V) for V = 25; 100; 625; 900; 2,500; and 10,000. Part 3. Plot the points from your table on the grid and sketch the graph. Part 4. If the graph were rotated 90° counterclockwise about the origin, which function would the result resemble? Explain your answers, including relating the two functions
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
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The volume of a cylindrical canister is given by the formula V=nr^2h Part1. Write a function f(V) to express the radius of the canister as a function of the volume. Part 2. Suppose a certain type of canister must have a height of 32 centimeters (cm), so the quantity nh is about 100 cm. Write an updated version of the function f(V), using 100 for nh, to determine the radius of the canister that would result in certain volumes. Complete the table to find the values of f(V) for V = 25; 100; 625; 900; 2,500; and 10,000. Part 3. Plot the points from your table on the grid and sketch the graph. Part 4. If the graph were rotated 90° counterclockwise about the origin, which function would the result resemble? Explain your answers, including relating the two functions
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