The base area of the cone is found by multiplying the radius squared by pi. In this case, the radius is 7 inches, so the base area is 49π square inches.
The lateral area of the cone is found by multiplying the radius, slant height, and pi. In this case, the radius is 7 inches and the slant height is 20 inches, giving a lateral area of 140π square inches.
Adding the base area and lateral area gives the total surface area of the cone, which is 189π square inches.
Approximating π as 3.14, the approximate numerical value for the surface area is 593.46 square inches.
Simplify these paragraphs in a few sentences: The base area of the cone is given by the formula A = πr^2, where r is the radius of the base of the cone. In this case, the diameter is given as 14 inches, so the radius is half of that, or 7 inches. Plugging this into the formula, we get A_base = π * (7 inches)^2 = 49π square inches.
The lateral area of the cone is given by the formula A = πrs, where r is the radius of the base and s is the slant height of the cone. In this case, the slant height is given as 20 inches, and the radius is 7 inches. Plugging these values into the formula, we get A_lateral = π * (7 inches) * (20 inches) = 140π square inches.
Adding the base area and the lateral area together, we get the total surface area of the cone peak: A_total = A_base + A_lateral = 49π + 140π = 189π square inches.
To get a more precise numerical value for the surface area, we can approximate π as 3.14: A_total ≈ 189 * 3.14 = 593.46 square inches
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