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)

Answer 1

The volume of a tennis ball can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3.

Given that the radius of each tennis ball is 2.5 in, the volume of one tennis ball is:
V_ball = (4/3)(3.14)(2.5^3) = 65.45 in^3.

If there are a dozen tennis balls in the container, the total volume occupied by the tennis balls is:
V_total = 12 * V_ball = 12 * 65.45 = 785.4 in^3.

The amount of space empty in the container is:
V_empty = V_container - V_total = 3200 - 785.4 = 2414.6 in^3.

Rounding to the nearest whole number, the empty space in the container is approximately 2415 in^3.