The volume of a container measures 3,200 in. Cubed and contained a dozen tennis balls. Each tennis ball has a radius of 2.5 in How much space in the container is empty
To find the space that is empty in the container, we need to subtract the total volume of the tennis balls from the volume of the container.
The volume of one 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 one tennis ball is:
V_ball = (4/3)π(2.5)^3
The volume of a dozen tennis balls (12 balls) is:
V_dozen_balls = 12 * V_ball
The volume of the container, given as 3,200 in^3, is:
V_container = 3,200 in^3
The empty space in the container can be found by subtracting the volume of the dozen tennis balls from the volume of the container:
Empty space = V_container - V_dozen_balls
Calculating this:
Empty space = 3,200 in^3 - 12 * [(4/3)π(2.5)^3] ≈ 3,200 in^3 - 12 * (4/3) * 3.1416 * 15.625 ≈ 3,200 in^3 - 12 * 65.449 ≈ 3,200 in^3 - 785.388
Empty space ≈ 2,414.612 in^3
Therefore, the empty space in the container is approximately 2,414.612 cubic inches.