Question 119669


given:

{{{r = 14 cm }}} 

chord of this circle subtends an angle of measure {{{120}}} at the centre

Find the {{{area}}} of the {{{minor}}}{{{ segment}}} formed by this chord

To find the area of a {{{minor}}}{{{ segment}}}(slice of cake)  think of it as a sector minus a triangle with vertices at the centre of the circle and at the end points of the chord.

Let the angle of the triangle at the centre of the circle be {{{x}}} 
degrees.  Then the area of the sector {{{A}}} is:

          {{{A  = pi * r^2 * (x/360)}}}

	
          {{{A  = 3.14 * (14cm)^2 * (120/360)}}}

          {{{A  = 3.14 * 196cm^2 * .33}}}

          {{{A  = 615.44cm^2 * .33}}}

          {{{A  = 203.0952cm^2 }}}