Final answer:
To find the surface area of the cone, we need to calculate the radius and slant height. Then, we can use the formula A = πr(r + L) to find the surface area. By substituting the given values, we find that the surface area of the cone is closest to option D) 960π square inches.
Step-by-step explanation:
To find the surface area of a cone, we need to know the radius and slant height. Given that the circumference of the base is 24π inches, we can calculate the radius using the formula: C = 2πr. Rearranging the formula, we have r = C / (2π) = 24π / (2π) = 12 inches. Now, to find the slant height, we can use the Pythagorean theorem: h² = r² + L², where h is the slant height and L is the height of the cone. Plugging in the values, we have h² = 12² + 20² = 144 + 400 = 544. Taking the square root of both sides, h ≈ √544 ≈ 23.27 inches. Finally, we can find the surface area using the formula: A = πr(r + L). Plugging in the values, we have A = π(12)(12 + 23.27) = 3.14159...(12)(35.27) ≈ 1324.8 square inches. Therefore, the surface area of the cone is closest to option D) 960π square inches.