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The volume of a container measures 3,200 in.3 and contains a dozen tennis balls. Each tennis ball has a radius of 2.5 in. How much space in the container is empty? Use 3.14 as an approximation for pi. Round to the nearest whole number, if necessary.(1 point)
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GPT 3.5
The volume of one tennis ball can be calculated using the formula for the volume of a sphere:
V = (4/3)*π*r^3
where V is the volume and r is the radius of the sphere.
Using a radius of 2.5 in and the approximation π ≈ 3.14, the volume of one tennis ball is:
V = (4/3)*3.14*(2.5^3)
V ≈ (4/3)*3.14*15.625
V ≈ 65.45
Since there are a dozen (12) tennis balls in the container, the total volume of the tennis balls is:
12 * 65.45 ≈ 785.4
To calculate the empty space in the container, we subtract the volume of the tennis balls from the total volume of the container:
3200 - 785.4 ≈ 2414.6
Therefore, there is approximately 2415 cubic inches of empty space in the container.
V = (4/3)*π*r^3
where V is the volume and r is the radius of the sphere.
Using a radius of 2.5 in and the approximation π ≈ 3.14, the volume of one tennis ball is:
V = (4/3)*3.14*(2.5^3)
V ≈ (4/3)*3.14*15.625
V ≈ 65.45
Since there are a dozen (12) tennis balls in the container, the total volume of the tennis balls is:
12 * 65.45 ≈ 785.4
To calculate the empty space in the container, we subtract the volume of the tennis balls from the total volume of the container:
3200 - 785.4 ≈ 2414.6
Therefore, there is approximately 2415 cubic inches of empty space in the container.