Question

A chord of a circle of radius $10$ cm subtends a right angle at the centre. Find the area of the corresponding major sector.

Answer 1

Radius $r=10cm$

angle$={90}^{\circ }$

area of sector $A=\frac{90}{360}\pi r^2$

A$=3.14\times 10\times \frac{10}{4}$

A$=25\times 3.14$

A$=78.5sq.cm$

Let the angle subtended and radius form an arc AOB, then

area of AOB$=r\times r\times \frac{sin90}{2}$

AOB$=10\times 10\times \frac{1}{2}$

ar. of AOB $=50sq.cm$

area of minor segment $=78.5-50$

$=28.5aq.cm$

Then the area of circle $=\pi r^2$

$=3.14\times 10\times 10$

$=314Sq.cm$

area of major segment =area of the circle -area of the minor segment

$=314-28.5$

$=285.5sq.cm$