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
Item 1
height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use (1 point)
The formula for the surface area of a cone is given by:
Surface Area = πr(r + √(r^2 + h^2))
In this case, the diameter of the cone is given as 14 inches, so the radius (r) is half of that, which is 7 inches. The height (h) is given as 20 inches.
By substituting these values into the formula, we get:
Surface Area = π(7)(7 + √(7^2 + 20^2))
Calculating the values inside the square root:
Surface Area = π(7)(7 + √(49 + 400))
Surface Area = π(7)(7 + √449)
Surface Area ≈ 3.14(7)(7 + 21.19)
Surface Area ≈ 3.14(7)(28.19)
Surface Area ≈ 615.38 square inches
Therefore, the surface area of the cone peak is approximately 615.38 square inches.