A chord with a length of $14$ runs from $pi/3$ to $pi/2$ radians on a circle. What is the area of the circle?

Question

1521 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-23T11:00:46

$=2246$

A chord travels $pi/2-pi/3=pi/6$ radians of the Circle

In other words chord travels $pi/6-:2pi=1/12 th$ of Circumference

Circumference $=2pir$ where $r=radius$

Therefore we can write

Length of the Chord $=14=(2pir)/12$

or

$2pir=14times12$

or

$r=168/(2pi)$

or

$r=26.74$

Area of the Circle $=pir^2$

$=pi(26.74)^2$

$=2246$

A chord with a length of 14 14 runs from pi/3 pi/3 to pi/2 pi/2 radians on a circle. What is the area of the circle?