Emily ordered paper sleeves for the sugar cones at her ice cream parlor.If the diameter of each sleeve is 47 Millimeters and the slant height is 112 millimeters,which is closet to the amount of paper used to make each sleeve
If you "open up" the paper cone you will have an obtuse-angled sector of a circle (looks like the old 'pac-man' shape)
the radius of that sector is 112 mm , and the circumference of the circular base of the cone becomes the arc length of the sector.
finding that arc length:
radius of base = 23.5 mm
circumference of base = 2π(23.5)
= 47π
= 147.6548... (I stored it in memory)
so arc length = 47π mm
circumference of the whole circle of the flattened out cone
= 2π(122)
= 244π
area of whole flattened-out cone
= π(112^2)
let the area of the sector be x
x/(π(112^2) = 47π/(244π)
x = (47/112)(112^2)π
= 47(112)π
= appr 16537 mm^2
check my arithmetic