Final answer:
The volume of a spherical hot air balloon with a diameter of 50 feet is approximately 65,417 cubic feet, calculated using the volume formula for a sphere.
Step-by-step explanation:
The volume of a spherical hot air balloon with a diameter of 50 feet is calculated using the formula for the volume of a sphere, which is V = 4/3 \( \pi \) r^3, where r is the radius of the sphere. Since the diameter is 50 feet, the radius (r) is half of that, which is 25 feet. By substituting the values into the formula and using 3.14 for \(\pi\), we get V = 4/3 * 3.14 * (25)^3.
Calculating the volume: V = 4/3 * 3.14 * 15625 ≈ 65,416.67 cubic feet. Thus, the nearest whole number is 65,417 cubic feet, which is the amount of air the balloon would contain.
Here is the step-by-step calculation:
1. Find the radius from the diameter: r = diameter / 2 = 50 / 2 = 25 feet.
2. Substitute the radius into the volume formula: V = 4/3 * 3.14 * (25)^3.
3. Calculate the cube of the radius: (25)^3 = 15625.
4. Calculate the volume: V = 4/3 * 3.14 * 15625 ≈ 65,416.67 cubic feet.