Eli is making a model castle out of clayOne of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3,14 for pi1 point)
To find the surface area of the cone peak, we need to find the area of the base and the area of the lateral surface.
The area of the base of a cone is given by the formula: A = πr², where r is the radius. Since we know the diameter is 14 inches, the radius is half of that, so r = 14/2 = 7 inches. Plugging this into the formula, we get A = π(7)² = 49π square inches.
The area of the lateral surface of a cone is given by the formula: A = πrℓ, where r is the radius and ℓ is the slant height. Plugging in the values, we get A = π(7)(20) = 140π square inches.
So, the total surface area of the cone peak is the sum of the base area and lateral surface area: 49π + 140π = 189π square inches.
To round this to the nearest hundredth, we can use the approximation 3.14 for π. Multiplying 3.14 by 189 gives us 594.66.
Therefore, the surface area of the cone peak is approximately 594.66 square inches.