Question

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

Answer 1

[AI-generated answer — Bot 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

V = 4/3 * π * (2.5)^3
V ≈ 4/3 * 3.14 * 15.625
V ≈ 4.19 * 15.625
V ≈ 65.51 in.^3

Since there are 12 tennis balls in the container, the total volume occupied by the tennis balls is:
12 * 65.51 ≈ 786.12 in.^3

To find the amount of empty space in the container, we subtract the volume occupied by the tennis balls from the total volume of the container:
3,200 - 786.12 ≈ 2,413.88 in.^3

Therefore, approximately 2,414 in.^3 of space in the container is empty.