Question

PLEASE HELP ME PLEASE (10 mins)

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

Answer 1

Explanation:

1) When the sector is cut out, the remaining sector would be used to form the cone. The angle subtended by this sector would be

360 - 60 = 300°

The length of the arc of this sector would represent the circumference of the circular base of the conical hat.

Radius of the circle = diameter/2 = 20/2 = 10 inches

Formula for length of arc = #/360 × 2πr

Where

# is the subtended angle

Therefore,

Length of arc = 300/360 × 2 × 3.14 × 10 = 52.3 inches

circumference of the circular base of the conical hat = 52.3 inches

2) the surface area = πrl

Where

l represents the slant height

the radius of the circle would become l.

To determine the radius of the cone, we would apply, we would make use of the circumference of the circular base.

Circumference = 2πr

52.3 = 2 × 3.14 × r

r = 52.3/6.28 = 8.33 inches

Surface area = 3.14 × 8.33 × 10 = 262 inches²