Question
The volume of a container measures 3200 in.^3 and contains a dozen tennis balls. Each tennis ball has a radius of 2.5 inches. How much space is the container empty. Use 3.14 as an approximation for pi
Answers
GPT 3.5
The volume of each tennis ball can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3, where r is the radius of the tennis ball.
Given that the radius of each tennis ball is 2.5 inches, the volume of each tennis ball is:
V = (4/3) * 3.14 * (2.5^3) = 4.19 * 15.625 = 65.35 in.^3 (approx.)
Since there are a dozen tennis balls, the total volume occupied by the tennis balls is:
65.35 * 12 = 784.2 in.^3 (approx.)
To find the volume of the empty space in the container, we deduct the volume occupied by the tennis balls from the volume of the container:
3200 - 784.2 = 2415.8 in.^3 (approx.)
Therefore, the container is empty with approximately 2415.8 in.^3 of space remaining.
Given that the radius of each tennis ball is 2.5 inches, the volume of each tennis ball is:
V = (4/3) * 3.14 * (2.5^3) = 4.19 * 15.625 = 65.35 in.^3 (approx.)
Since there are a dozen tennis balls, the total volume occupied by the tennis balls is:
65.35 * 12 = 784.2 in.^3 (approx.)
To find the volume of the empty space in the container, we deduct the volume occupied by the tennis balls from the volume of the container:
3200 - 784.2 = 2415.8 in.^3 (approx.)
Therefore, the container is empty with approximately 2415.8 in.^3 of space remaining.