Question

In a circle of radius 10.5 cm, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

Answer 1

the radius of the circle r = 10.5 cm
and the minor arc is one-fifth of the major arc.
let the major arc subtend the angle $\theta$ on the circumference.
therefore minor arc subtend angle (360 - $\theta$) on the circumference.
minor arc = major arc

$2\pi r\times \frac{360-\theta }{360}=\frac{1}{5}\times 2\pi r\times \frac{\theta }{360}$

5(360−$\theta$)=$\theta$

1800−5$\theta$=$\theta$

6$\theta$=1800
$\theta$=300

therefore the area of the sector corresponding to the major arc
=
=
=

= 288.75