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)
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.