Mathematics

Problem

A garden sprinkler is fixed at a point and sprays water up to a distance of

10\,\text{m}

. It oscillates continuously from

30^{\circ}

east of north to

30^{\circ}

west of north and back, completing 15 such full swings every minute. Use

\pi=\tfrac{22}{7}

. a. (i) Find the area of the ground watered in one complete swing. b. (ii) Determine the total area watered in

30\,\text{minutes}

. c. (iii) If the lawn requires a water depth of

6\,\text{mm}

, calculate the total volume of water (in litres) delivered in the

30\,\text{minute}

period. [

1\,\text{m}^{3} = 1000\,\text{litres}

]