Question

A chord of a circle subtends an angle 60 degrees at the centre. If the length of the chord is 100cm find the area of the major segment.

Answer 1

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Answer 2

Answer:

0.2653 $m^2.$

Step-by-step explanation:

As given in question,

Angle subtends by the chord at the centre of the circle,

$\theta\ =\ 60^o$

           $=\ \dfrac{\pi}{3}\ rad$

length of the chord, l = 100 cm

                                   = 1 m

From the relation,

     $\theta\ =\ \dfrac{l}{r}$

$=>\ \dfrac{\pi}{3}\ =\ \dfrac{1}{r}$

$=>\ r\ =\ \dfrac{1}{\pi}$

angle made by a complete circle on its centre is 360°.

Since, here angle made by minor segment is 60°, hence the angle made by the major segment is 300°.

Hence, the area of major segment can be given by

$A\ =\ \dfrac{300}{360}.\pi .r^2$

    $=\ \dfrac{5}{6}\times \pi .(\dfrac{1}{\pi})^2$

    $=\ 0.2653\ m^2$

Hence, the area of major segment will be 0.2653 $m^2.$