Respuesta :
Answer:
21806 basketballs are needed to fill the gym
Step-by-step 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
[tex]V = 96*53*30 = 152640[/tex] cubic inches
Volume of the basketball:
The basketball is an sphere, so its volume is
[tex]V = \frac{4\pi r^3}{3}[/tex]
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:
[tex]V = \frac{4\pi (1.1875)^3}{3} = 7[/tex] 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
