SOLUTION: 20. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm. htt

Algebra ->  Volume -> SOLUTION: 20. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm. htt      Log On


   

Question 612061: 20. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.

https://www.connexus.com/content/media/461958-3232011-35122-PM-1691221172/res00000/ppg/examview/S_GEOMB_05_Unit_Test/ot020-1.jpg

a. What is the volume of the cylinder rounded to the nearest cubed centimeter?
b. What is the total volume of the three balls rounded to the nearest cubed centimeter ?
c. What percent of the volume of the container is occupied by the three balls?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The height of the cylinder (h) is three time the diameter of each ball, or:
h+=+3%2813%29cm.
h+=+39cm.
The radius of the cross-section of the cylinder is the same as the radius of a ball, or:
r+=+13%2F2
r+=+6.5cm.
a) The volume of the cylinder is:
V%5Bc%5D+=+%28pi%29r%5E2%2Ah Substitute r+=+6.5,h+=+39 and use pi+=+3.14 as an approximation.
V%5Bc%5D+=+%283.14%29%286.5%29%5E2%2839%29
V%5Bc%5D+=+5173.935cu.cm. Round to nearest cubic cm. to get:
V%5Bc%5D+=+5174cu.cm.
b) The total volume of the three balls is:
V%5Bb%5D+=+3%284%2F3%29%28pi%29r%5E3
V%5Bb%5D+=+4%283.14%29%286.5%29%5E3
V%5Bb%5D+=+3449.29cu.cm. Round the nearest cubic cm. to get:
V%5Bb%5D+=+3449cu.cm.
c) The percent volume of the container occupied by the three balls is:
V+=+%283449%2F5174%29%2A100
V+=+66.66%25%