Question

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.

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 1

A: 5177 cm^3

B: 3449 cm^3

C: 66%

Explanation:

3.14 x (13/2)^2 x (13 x 3) = 5176.56 -> 5177 cm ^3

(4/3 x 3.14 x (13/2)^3) x 3 = 3449.29 -> 3449 cm^3

3449/5177 = 0.66 -> 66%

Answer 2

So lets get one by one:

a) height = 3 * diameter
cross section area = pi (diameter/2)^2
Volume = 3/4 pi diameter^3

b) volume of 3 balls = 3 * 4/3 pi (diameter/2)^3
=1/2 pi diameter^3

c) The ratio is the answer to b over the answer to a
= (1/2) / (3/4) = 2/3
I hope this is what you were looking for.