(a) Prove that the area of a sector of a circle of radius and central angle (in…

MATHEMATICS · Subjective · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles

Problem

(a) Prove that the area of a sector of a circle of radius

r

and central angle

\theta

(in degrees) bears the same ratio to the area of the entire circle as

\theta : 360

. (b) Hence obtain an expression for the area of the sector in terms of

r

and

\theta

. (c) Using the result obtained in part (b), find the area of a sector of a circle of radius

7\,\mathrm{cm}

and central angle

150^{\circ}

. (d) Determine the length of the arc that encloses this sector.