Answer:
1. The circumference of the circular base of the conical hat is 52.36 inches
2. The surface area of the cone that needs to be covered is 262 in.²
Step-by-step explanation:
Here we have that the given parameters are;
Diameter, D of circular = 20 in. = 2 × radius R, of the circle
R = 10 in.
Cut out section of cut out sector of circle = 60°
Therefore, circumference of the circular base = π×D×(360 - 60)/360 which gives;
The circumference of the circular base of the conical hat = π×20×(30)/36 = π·50/3 = 52.36 in.
Therefore, the radius of the formed cone = π·50/3/(2·π) = 25/3 = [tex]8\tfrac{1}{3}[/tex] = 8.33 in.
The formed cone satisfies the equation;
R² = h² + r²
Where:
h = Height of the cone
r = radius of the cone
∴ 10² = h² + 8.33²
∴ h² = 10² - 8.33² = 30.56 in.
The lateral surface area of the cone = π×r×l where l = R, we therefore have;
The lateral surface area of the cone = π×8.33×10 = [tex]\pi \cdot 8\tfrac{1}{3}[/tex] = 261.8 in.² = 262 in.².
The surface area of the cone that needs to be covered = The lateral surface area of the cone = 262 in.².
