Subjects geometry

Sphere Area A55732

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Find the lateral area and total surface area of a sphere with radius $r=11$ ft. 2. **Recall formulas:** - The lateral area of a sphere is the same as its total surface area because a sphere has no lateral surface distinct from its total surface. - The formula for the surface area of a sphere is $$A = 4\pi r^2$$ 3. **Calculate the surface area:** $$A = 4\pi (11)^2 = 4\pi \times 121 = 484\pi$$ 4. **Evaluate the numerical value:** Using $\pi \approx 3.1416$, $$A \approx 484 \times 3.1416 = 1520.53$$ 5. **Interpretation:** - The lateral area is not distinct for a sphere, so it is "None" or not applicable. - The total surface area is approximately $1520.53$ ft$^2$. **Final answer:** Lateral Area = None; Total Area $\approx 1520.53$ ft$^2$ (Option C)
11 ft