Question

Volume of a container measures 3,200 in^3 and contains a dozen tennis balls each ball has a radius of 2.5 in how much space in the container is empty use 3.14 for pi.

Answer 1

First, let's calculate the volume of 12 tennis balls. The formula for the volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere.

The volume of one tennis ball is:
V_ball = (4/3) * 3.14 * (2.5)^3
V_ball = (4/3) * 3.14 * 15.625
V_ball = 62.833 in^3

Since there are 12 tennis balls in the container, the total volume occupied by the tennis balls is:
V_total_balls = 12 * V_ball
V_total_balls = 12 * 62.833
V_total_balls = 753.996 in^3

To find the empty space in the container, we subtract the total volume occupied by the tennis balls from the total volume of the container:
Empty space = 3,200 - 753.996
Empty space = 2,446.004 in^3

Therefore, there are approximately 2,446.004 cubic inches of empty space in the container.