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.

radius of the circle r = 10.5 cm
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
$2\pi r*\frac{360-\theta }{360}=\frac{1}{5}*2\pi r*\frac{\theta }{360}\phantom{\rule{0ex}{0ex}}5\left(360-\theta \right)=\theta \phantom{\rule{0ex}{0ex}}1800-5\theta =\theta \phantom{\rule{0ex}{0ex}}6\theta =1800\phantom{\rule{0ex}{0ex}}\theta =\frac{1800}{6}=300$
therefore the area of the sector corresponding to the major arc

hope this helps you.

• 11

minor arc=1/5 of major arc

by applying ar of the arc for the minor arc

teta/360*2*22/7*10.5

since the minor arc is 5 times th majorthe angle is

360/5=72

substituting this in formulae

we get

13.2cm

now find circumfrence of the circle 2*pie*r

2*22/7*10.5=66cm

now since minor arc is 13.2 and cis 66

therefor major arc is 66-13.2=52.8

i think it helped u

in case of help pls ask

• -5
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