For a certain logo

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

Problem

For a certain logo, a sector of a circle has an arc length of 22 cm and an area of

154\,\text{cm}^2

. The sector’s centre and boundaries form a single continuous piece of metal. (a) Form an equation involving the radius

r

and central angle

\theta

(in degrees) using the information about arc length. (b) Form a second equation involving

r

and

\theta

using the information about the area of the sector. (c) Solve the simultaneous equations obtained in parts (a) and (b) to find the exact values of

r

and

\theta

. (d) Using the values of

r

and

\theta

, determine the perimeter of the metal piece (include the two straight sides and the curved edge).