The sphere's surface area, calculated using the formula 4πr^2 with a diameter of 30 feet, is approximately 262.3038 square meters after converting units.
1: Understand the Formula
The formula for the surface area of a sphere is given by 4πr^2, where r is the radius of the sphere.
2: Convert Diameter from Feet to Meters
Given diameter: 30 feet
To convert feet to meters, we use the conversion factor 1 foot = 0.3048 meters.
Diameter in meters = 30 feet * 0.3048 meters/foot
Diameter in meters ≈ 9.14 meters
3: Find the Radius
The radius (r) is half of the diameter.
r = Diameter / 2
r = 9.14 meters / 2
r ≈ 4.57 meters
4: Apply the Formula
Now, plug the radius into the surface area formula:
Surface Area = 4π * (4.57)^2
5: Perform the Calculation
Surface Area ≈ 4π * 20.8849
Surface Area ≈ 83.5396π
6: Approximate the Result
Surface Area ≈ 83.5396 * 3.14159
Surface Area ≈ 262.3038 square meters
7: Final Conclusion
The surface area of the sphere is approximately 262.3038 square meters.