Question

question 5 (mc) (05.02 mc) a cylinder has an 18 - 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. o 1,152pi in³ o 1,179pi in³ o 1,215pi in³ o 1,251pi in³

Explanation:

Step1: Calculate the volume of the cylinder

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. The diameter of the cylinder is 18 inches, so the radius $r = \frac{18}{2}=9$ inches and the height $h = 15$ inches. Then $V_{cylinder}=\pi\times9^{2}\times15=\pi\times81\times15 = 1215\pi$ cubic - inches.

Step2: Calculate the volume of the ball

The formula for the volume of a sphere (ball) is $V_{sphere}=\frac{4}{3}\pi r^{3}$. The diameter of the ball is 6 inches, so the radius $r=\frac{6}{2} = 3$ inches. Then $V_{sphere}=\frac{4}{3}\pi\times3^{3}=\frac{4}{3}\pi\times27 = 36\pi$ cubic - inches.

Step3: Calculate the volume of water

The volume of water in the cylinder is the volume of the cylinder minus the volume of the ball. So $V = V_{cylinder}-V_{sphere}=1215\pi-36\pi=1179\pi$ cubic - inches.

Answer:

$1,179\pi\ in^{3}$