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

Answer:

a) 5177

b) 1150

c)66.67%

Step by step explanation:

a) Based on the known dimensions of the balls, you know that the height of the container is 13*3=39 cm, while the radius is 13/2=6.5cm. Using the formula for the volume of a cylinder, you get $\pi r^2 h= \pi \cdot 6.5^2 \cdot 39\approx 5177$ cubic centimeters.

b) The volume of a single one of the balls can be found with the formula for the volume of a sphere, or $\frac{4}{3}\pi r^3$, or in this case about 1150 cubic centimeters. Multiplying this by 3, you get about 3451 cubic inches.

c) 3451/5177 is almost exactly 2/3, or about 66.67%. Hope this helps!