An irrigation sprinkler rotates through an angle of and sprays water up to a distance…

MATHEMATICS · Multi-part · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles

Problem

An irrigation sprinkler rotates through an angle of

40^{\circ}

and sprays water up to a distance of

r

metres, covering an area of

242\,\text{m}^2

on the ground during one complete rotation. (i) Find the value of

r

correct to two decimal places. (ii) Determine the length of the ground surface traced by the tip of the water jet in one rotation.