Answer:
Step-by-step 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
