Calculate the volume of the gym.
The volume of a rectangular prism is given by the formula V = length * width * height. Plugging in the given values, we have V = 52 ft * 75 ft * 21 ft = 82,950 ft^3. Calculate the volume of a single balloon.
The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius of the sphere. Plugging in the given radius of 0.35 ft, we have V = (4/3) * π * (0.35 ft)^3 ≈ 0.179 ft^3. Divide the volume of the gym by the volume of a single balloon.
Dividing the volume of the gym (82,950 ft^3) by the volume of a single balloon (0.179 ft^3), we get 82,950 ft^3 / 0.179 ft^3 ≈ 463,687.15. Round the result to the nearest whole number.
Rounding 463,687.15 to the nearest whole number, we get 463,687. So the answer is 463,687
