Jessica wants to dress up as a witch for a costume party. She is making her own costume. She wants a hat with a slant height of 14 inches and a base radius of 9 inches. What is the lateral area of her hat?

A) 396 in squared

B) 254 in squared

C) 198 in squared

D) 63 in squared

pwolfey
Nov 2, 2017

#1**+2 **

Her hat is a cone. If you "unfold" a cone, it makes a sector of a circle.

lateral area of cone = area of sector

area of sector / area of circle = circumference of base / circumference of circle

area of sector / [pi * 14^{2}] = [2pi * 9] / [2pi * 14]

area of sector / [pi * 14^{2}] = 9 / 14

area of sector = [pi * 14^{2}] * 9/14 = 126pi

≈ 396 in^{2}

hectictar
Nov 3, 2017

#1**+2 **

Best Answer

Her hat is a cone. If you "unfold" a cone, it makes a sector of a circle.

lateral area of cone = area of sector

area of sector / area of circle = circumference of base / circumference of circle

area of sector / [pi * 14^{2}] = [2pi * 9] / [2pi * 14]

area of sector / [pi * 14^{2}] = 9 / 14

area of sector = [pi * 14^{2}] * 9/14 = 126pi

≈ 396 in^{2}

hectictar
Nov 3, 2017