Elias making a model Castle at a clay. One of the roof peeks is in the shape of a comb of the diameter of 14 in a slant height of 20 in what is the surface area of the cone peak use 3.14 for pi

Answer 1

The formula for the surface area of a cone is:

SA = πr² + πr√(r² + h²)

Where:
- r is the radius (half of the diameter)
- h is the slant height

Given:
- Diameter = 14 inches
- Radius (r) = 14/2 = 7 inches
- Slant height (h) = 20 inches

Substitute the values in the formula:

SA = π(7)² + π(7)√(7² + 20²)
SA = π(49) + π(7)√(49 + 400)
SA = 49π + 7π√449
SA = 49π + 7π(21.1896)
SA = 49π + 148.326

Now, calculate the surface area:

SA ≈ 49(3.14) + 148.326
SA ≈ 153.86 + 148.326
SA ≈ 302.186 square inches

Therefore, the surface area of the cone peak in Elias's model castle is approximately 302.186 square inches.