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

and 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 = 1/5* major arc

$2\pi r*\frac{360-\theta}{360}=\frac{1}{5}*2\pi r*\frac{\theta}{360}\phantom{\rule{0ex}{0ex}}5(360-\theta )=\theta \phantom{\rule{0ex}{0ex}}1800-5\theta =\theta \phantom{\rule{0ex}{0ex}}6\theta =1800\phantom{\rule{0ex}{0ex}}\theta =\frac{1800}{6}=300$

therefore the area of the sector corresponding to the major arc

$=\pi {r}^{2}*\frac{\theta}{360}\phantom{\rule{0ex}{0ex}}=\frac{22}{7}*10.5*10.5*\frac{300}{360}\phantom{\rule{0ex}{0ex}}=33*10.5*\frac{5}{6}\phantom{\rule{0ex}{0ex}}=288.75c{m}^{2}$

hope this helps you.

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