# Ok, what am I doing wrong??

• Sep 23rd 2006, 08:33 AM
classicstrings
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

• Sep 23rd 2006, 09:03 AM
Plato
I get theta to be 0.72 or 36/50.
Using that value the area is 75.769.
• Sep 23rd 2006, 09:52 AM
Soroban
Hello, classicstrings!

Quote:

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 .= .

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