A cylindrical can has a radius of 4 inches and a height of 12 inches. A spherical ball is placed on the bottom of the can, then water is poured into the can. The ball does not float.

Suppose the ball has a radius of 1 inch. What volume of water, in cubic inches, must be poured into the can so that the water level equals the height of the ball?

923?923? cubic inches

Suppose the ball has a radius of r? inches. Write a function for the volume of water required to make the water level equal the height of the ball as a funciton of the radius of the ball.

Suppose you wanted to known the radius of the ball that will require the most amount of water to make the water level equal the height of the ball.

Which of the following is the goal of the described situation?

Write the function that describes the rate of change of the volume of water with respect to the radius of the ball.

V'(r)=??(?)=

What is the radius required to maximize the volume of water?

inches

What is the maximum volume of water required to make the water level equal to the height of the ball?

cubic inches

• Minmize the radius of the ball.
• Maximize the height of the water.
• Maximize the radius of the ball.
• Maximize the volume of water.
• Minimize the volume of water.

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