Final answer:
To find out how many basketballs can fit inside the gym, we need to calculate the volume of the gym and the volume of a basketball. The volume of the gym is 314,160,768 cubic inches and the volume of a basketball is 408.888 cubic inches. Dividing the volume of the gym by the volume of a basketball, approximately 768,266 basketballs can fit inside the gym with a radius of 4.7 inches.
Step-by-step explanation:
To find out how many basketballs can fit inside the gym, we need to calculate the volume of the gym and the volume of a basketball. The volume of a rectangular prism, which represents the gym, can be calculated by multiplying its length, width, and height. The volume of a basketball, which approximates a sphere, can be calculated by using the formula (4/3) * pi * radius^3. Once we have both volumes, we can divide the volume of the gym by the volume of a basketball to find the number of basketballs that can fit inside.
The length of the gym is 96 feet, the width is 62 feet, and the height is 31 feet. To convert these measurements to inches, we multiply each measurement by 12 since there are 12 inches in a foot. So the length becomes 1152 inches, the width becomes 744 inches, and the height becomes 372 inches.
The radius of the basketball is given as 4.7 inches. To calculate the volume of the gym, we multiply the length, width, and height: 1152 * 744 * 372 = 314,160,768 cubic inches. To calculate the volume of a basketball, we substitute the radius into the formula: (4/3) * pi * (4.7^3) = 408.888 cubic inches.
Finally, we can divide the volume of the gym by the volume of a basketball: 314,160,768 / 408.888 ≈ 768,266.36.
Approximately 768,266 basketballs with a radius of 4.7 inches can fit inside the gym.