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
a. The diameter of the balls is 13 cm, so the radius is half of that, which is 6.5 cm. The height of the cylinder is equal to the diameter of the balls, which is 13 cm.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Plugging in the values, we get:
V = π(6.5)^2(13)
V ≈ 1681 cm^3
Therefore, the volume of the cylinder is approximately 1681 cubic centimeters.
b. The volume of each ball is given by the formula V = (4/3)πr^3.
Plugging in the values, we get:
V = (4/3)π(6.5)^3
V ≈ 1436 cm^3
Since there are three balls, the total volume of the three balls is:
3*1436 = 4308 cm^3
Therefore, the total volume of the three balls is approximately 4308 cubic centimeters.
c. The percentage of the volume occupied by the three balls is given by (total volume of the balls / volume of the cylinder) * 100.
Plugging in the values, we get:
Percentage = (4308 / 1681) * 100
Percentage ≈ 256.5%
Therefore, approximately 256.5% of the volume of the container is occupied by the three balls.