Question

Can ya help?
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.

Please explain this process.

Answer 1

First decide whether you want just the outside (lateral) area of the cone (typical for a roof peak) or the total surface area including the circular base. A roof peak usually uses only the lateral area, so I'll compute that and also show the total-area option.

1) Lateral surface area (typical for a roof peak)
- Radius r = diameter/2 = 14/2 = 7 in.
- Slant height l = 20 in.
- Lateral area = π r l = 3.14 × 7 × 20 = 3.14 × 140 = 439.6 in².
- Rounded to the nearest hundredth: 439.60 in².

2) (Optional) Total surface area including the base
- Total area = π r l + π r² = π r (l + r) = 3.14 × 7 × (20 + 7) = 3.14 × 7 × 27 = 3.14 × 189 = 593.46 in².

Answer (lateral area, roof peak): 439.60 in².