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.
The formula for the surface area of a cone is given by:
Surface Area = πr(r + l)
where r is the radius of the base and l is the slant height.
Given that the diameter of the base is 14 inches, the radius would be half of that, which is 7 inches. Therefore, the surface area is:
Surface Area = 3.14 * 7 * (7 + 20)
Surface Area = 3.14 * 7 * 27
Surface Area = 5919.06
Rounded to the nearest hundredth, the surface area of the cone peak is approximately 5919.06 square inches.