Read the statements below and answer the questions that follow
MATHEMATICS · Subjective · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles
Problem
Read the statements below and answer the questions that follow.
(i) Explain why the ratio of the length of an arc of a circle to the circumference of the entire circle is equal to the ratio of the central angle subtended by the arc to 360∘.
(ii) Hence derive a formula for the central angle θ (in degrees) in terms of the arc length L and the radius r.
(iii) A circular track has radius 70 m. A runner completes a bend whose arc length is 88 m. Using the formula derived in part (ii), calculate the angle through which the runner has turned.
(iv) Find the area of the sector swept out by the runner while negotiating the bend.