Question

The gym is 96 feet long 53 feet wide and 30 feet high. A bosketball is 28.5 inches

in diameter. How many basketballs are needed to fill the gym?

Answer 1

21806 basketballs are needed to fill the gym

Explanation:

We have to find both volumes in the same units, so I will use feet for the dimensions, the volume will be in cubic feet. Each feet has 12 inches.

Volume of the gym:

The volume of the gym(rectangular base with height) is given by the multiplication of its dimensions. So

`V = 96*53*30 = 152640` cubic inches

Volume of the basketball:

The basketball is an sphere, so its volume is

`V = (4\pi r^3)/(3)`

In which r is the radius, which is half the diameter.

28.5 inches in diameter, so 2.375 feet in diameter, radius of 1.1875 feet. The volume of the basketball is:

`V = (4\pi (1.1875)^3)/(3) = 7` cubic inches

How many basketballs are needed to fill the gym?

This is given dividing the volume of the gym by the volume of a basketball. So

152640/7 = 21805,7

Rouding up

21806 basketballs are needed to fill the gym