Eli making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches in a slant height of 20 inches. What is the surface area of the cone peak? Explain why the IS answer 593.46 and NOT 595.14

Answer 1

To find the surface area of the cone peak, we need to calculate the lateral area and the base area separately and then add them together.

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.

Therefore, the surface area of the cone peak of Eli's model castle made of clay is approximately 593.46 square inches, not 595.14.