Question

Express answer in exact form.

Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.


help me please

Answer 1

this is the same problem.. stuck from sooo many days.. right?

Answer 2

do u want the answer in pi-form?

Answer 3

yeah ineed hep

Answer 4

Area = 64pi - (128pi^3-96root3)/6

Answer 5

When the radius of the circle is 8" and chord length is also 8" Then this chord forms an equilateral triangle a the center . The angle subtended by the chord/arc at the center is also 60° or π/3 radians
Area of the larger segment = Area of the circle − area of the smaller segment
Area of the smaller segment = Area of the sector − area of the equilateral triangle formed by the chord at the center
Area of a sector = ½ R² θ where θ is the angle in radians subtended by the arc at the center of the circle =½×8²×π/3=32π/3 inch ²
Area of equilateral triangle of side 8 "=½×8×8sin60° =32×√3/2 =16√3 inch² Hence Area of the smaller segment = 32π/3 − 16√3
Area of the circle =πR²=π×8²=64π inch²
Hence area of larger segment =Area of the circle − area of the smaller segment
=64π−{32π/3 − 16√3}= 160π/3 + 16√3 inch²