Question

NEED HELP GEOMETRY ASAP

1. What is the circumference, in inches, of the circular base of the conical hat? Round to the nearest tenth.


2. You want to cover the top of the hat with fabric. What is the surface area, in square inches, that you will cover? (Do not include the base of the cone) Round to the nearest square inch.

Answer 1

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

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 =
`8\tfrac{1}{3}` = 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 =
`\pi \cdot 8\tfrac{1}{3}` = 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.