Eli is 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 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 pi.(
To find the surface area of the cone peak, we need to find the area of the curved surface (the lateral area) and add the area of the base.
First, we find the slant height (l) of the cone using the Pythagorean theorem:
l = sqrt(r^2 + h^2)
l = sqrt(7^2 + 20^2)
l = sqrt(49 + 400)
l = sqrt(449)
l ≈ 21.19 inches
Next, we find the lateral area of the cone using the formula:
Lateral area = π × r × l
Lateral area = 3.14 × 7 × 21.19
Lateral area ≈ 146.72 sq inches
Finally, we find the total surface area of the cone peak by adding the area of the base:
Total surface area = Lateral area + π × r^2
Total surface area ≈ 146.72 + 3.14 × 49
Total surface area ≈ 146.72 + 153.86
Total surface area ≈ 300.58 sq inches
Therefore, the surface area of the cone peak is approximately 300.58 square inches.