Question

question 2
a cylinder has a 12 - inch diameter and is 15 inches tall. it is filled to the top with water. a 6 - inch - diameter ball is placed within the cylinder, and then the cylinder is filled with water. how much water is in the cylinder? give your answer in terms of pi.

Explanation:

Step1: Calculate cylinder volume

The formula for the volume of a cylinder is $V_{cylinder}=\pi r_{cylinder}^2h$. Given the diameter of the cylinder $d_{cylinder} = 12$ inches, so the radius $r_{cylinder}=\frac{d_{cylinder}}{2}=6$ inches and height $h = 15$ inches. Then $V_{cylinder}=\pi\times6^{2}\times15=\ 540\pi$ cubic - inches.

Step2: Calculate ball volume

The formula for the volume of a sphere (ball) is $V_{ball}=\frac{4}{3}\pi r_{ball}^3$. Given the diameter of the ball $d_{ball}=6$ inches, so the radius $r_{ball}=\frac{d_{ball}}{2} = 3$ inches. Then $V_{ball}=\frac{4}{3}\pi\times3^{3}=36\pi$ cubic - inches.

Step3: Calculate water volume

The volume of water in the cylinder is the volume of the cylinder minus the volume of the ball. So $V_{water}=V_{cylinder}-V_{ball}=540\pi - 36\pi=504\pi$ cubic - inches.

Answer:

$504\pi$ cubic - inches