a sector of a circle is used to make a hat shaped like a right cone. the cone has a height of 4 in. and a base diameter of 8 inches. the outside of the hat is to be covered in red crepe paper. determine the area that will be covered in crepe paper to the nearest square inch.
+128473 We can use the Pythagorean Theorem to find the "slant height" of the cone....note that the raduis of the cone = 4 inches
Slant Height = sqrt [ height^2 + radius^2] = sqrt [ 4^2 + 4^2 ] = sqrt [ 16 + 16 ] = sqrt [ 32] = 4sqrt (2) inches
The amount of crepe paper needed = the surface area of the cone = pi * radius * slant height =
pi * (4 inches) ( 4 sqrt (2) inches) =
pi * 16 sqrt (2) inches ^2 ≈ 71.086 in^2
