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Describe how the volume of three tennis balls, each with a diameter of 2.7​​ inches compares to the volume of their packaging, which is a cylinder that has the same diameter and a height of 8.1 inches. Explain or show your work.

User Cloxure
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1 Answer

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Answer:

Explanation:

The volume of the three tennis balls combined is approximately 4.88 cubic inches. The volume of the packaging cylinder is approximately 50.33 cubic inches. Thus, the volume of the three tennis balls is about 9.7% of the volume of their packaging cylinder.

To calculate this, we can use the formula for the volume of a sphere (V = 4/3 x π x r3) and the formula for the volume of a cylinder (V = π x r2 x h).

The radius of each tennis ball is half the diameter, or 1.35 inches. So, the volume of each tennis ball is 4/3 x π x (1.35)3 = 4.88 cubic inches.

The radius of the cylinder is the same as the diameter of each tennis ball, or 2.7 inches. The height of the cylinder is 8.1 inches. So, the volume of the cylinder is π x (2.7)2 x 8.1 = 50.33 cubic inches.

The volume of the three tennis balls is 4.88 x 3 = 14.64 cubic inches. The volume of the packaging cylinder is 50.33 cubic inches. Thus, the volume of the three tennis balls is 14.64 ÷ 50.33 = 0.097 = 9.7% of the volume of their packaging cylinder.

User Nickcan
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