You are making cone-shaped hats for a drama production. The pattern calls for circles with a 20-inch diameter. You are to cut out a sector created by a 60° angle

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 Relevance

1)

Circumference of the circular pattern: 20 * pi

After removing the 60 degree sector: 20 * pi * (1 - (60/360)) = (100/6)*pi

=~ 52.359877559829887307710723054658 inches

Round that off to 52.4

2)

Area of the circular pattern: pi * (20/2)^2 = 100*pi

After removing the 60 degree sector: 100 * pi * (1 - (60/360)) = (250/3)*pi

=~ 261.79938779914943653855361527329 square inches

Round that off to 262

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• 1.)

given

C = 2πr

C = 2π(20/2) = 62.8 in

2.)

θ = 360 - 60 = 300°

As = θ/(2π)πr^2

As = 300/360 π(10)^2

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• 1) 60° = π/3 radians

Circumference = 10(2π - π/3) = 50π/3 ≈ 52.360 inches

Ans: 52.4 inches

2) The area of a circular segment is A = r²Θ/2

The sector used for the hat has an included angle of 2π -π/3 = 5π/3

A = Θr²/2 = 5πr²/6 ≈ 500π/6 ≈ 261.799 sq in

Ans: 262 sq in.

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• Hint:

1/

the circumference of the circular base = arc of the sector

2/

the surface area=area of the sector

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