a. The diameter of each ball is 18 cm, so the radius of each ball is 9 cm. Since the balls just touch the top, bottom, and sides of the cylinder, the radius of the cylinder is equal to the radius of the balls, which is 9 cm.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Plugging in the values, V = π(9^2)h = 81πh
Since the balls just touch the top and bottom of the cylinder, the height of the cylinder is equal to the diameter of the ball, which is 18 cm.
Therefore, V = 81π(18) ≈ 4577.6 cm^3
b. The volume of each ball is V = (4/3)πr^3 = (4/3)π(9^3) = 3053.6 cm^3
The total volume of the three balls is 3 * 3053.6 = 9160.8 cm^3.
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 18 cm. a. What is the volume of the cylinder rounded to the nearest tenth? b. What is the total volume of the three balls rounded to the nearest tenth?
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