Question

OPQ is sector of a circle , with center at O and radius 18 cm. if angle POQ = 30° find the area in closed by arc PQ and chord PQ​

Answer 1

Answer:The required area is 2.68 square cm.

Step-by-step explanation:Area of sector POQ

=\frac{\theta}{360}*\pi\:r^2

=\frac{30}{360}*\frac{22}{7}*15*15

=\frac{1}{12}*\frac{22}{7}*225

=\frac{1}{6}*\frac{11}{7}*225

=\frac{2475}{42}\:cm^2

Area of triangle POQ

=\frac{1}{2}*a*b*sinC

=\frac{1}{2}*r*r*sin30

=\frac{1}{2}*15*15*\frac{1}{2}

=\frac{225}{4}

The area enclosed by arc PQ and Chord PQ

=​Area of sector POQ-Area of triangle POQ

=\frac{2475}{42}-\frac{225}{4}

=\frac{4950}{84}-\frac{4725}{84}

=\frac{4950-4725}{84}

=\frac{225}{84}

=2.68\:cm^2