Thread: Ok, what am I doing wrong??

Find the area of the minor segment formed on an arc of length 36cm drawn on a circle of radius 50cm.

Chord length = 2rsin(theta/2)
2 * 50sin(theta/2) = 36
theta = 0.7365

Area of segment = 0.5r^2(theta-sintheta)
= 81.01cm^2

Correct answer = 75.77cm^2

I get theta to be 0.72 or 36/50.
Using that value the area is 75.769.

Hello, classicstrings!

Find the area of the minor segment formed on an arc of length 36cm
drawn on a circle of radius 50cm.

Why are you playing with a chord?

Code:

               36
              * * *
          *           *
       *                 *
      * - - - - - - - - - *
        \               /
          \           /
            \       / 50
              \ θ /
                *

Arc length formula: .s .= .rθ

We have: .s = 36, r = 50

. . Hence: .36 = 50θ . →. θ = 0.72 (radians)


Area of a sector: .A .= .½r²θ

. . We have: . A .= .½(50²)(0.72) .= .900 cm²


Area of triangle: .½(50²)sin(0.72) .≈ .824.23 cm²


. . Therefore: .Area of segment .= .900 - 824.23 .= .75.77 cm²