178k views
2 votes
A lawn sprinkler located at the corner of a yard is set to rotate through 90° and project water out 10.5 metres. Find thefollowing, each to 3 significant figures:a.How much of the lawn is watered by the sprinkler?b. How far does the spray of water travel as the sprinkler rotates through its path?C.What is the distance around the edge of the watered area?

User Bor Laze
by
4.5k points

1 Answer

1 vote

The sprinkler covers the quarter area of a circle whose radius is 10.5 m.

The area of the quarter of circle is,


A=(\pi)/(4)(r)^2

Substitute the value of r in the equation to obtain the value area of lawn watered by sprinkler.


\begin{gathered} A=(\pi)/(4)\cdot10.5\cdot10.5 \\ =86.590 \end{gathered}

So answer of a part is 85.590 meter square.

(b)

The sprinkler water travel a distance of 10.5 m from the sprinkler. So answer of b part is 10.5m.

(c)

The distance of edge araound the water area is equal to the circumferencr of quarter circel.

The formula for the circumference of quarter circle is,


C=(\pi)/(2)r

Substitute the value of r in the equation to obtain the distance around the edge of watered area.


\begin{gathered} C=(\pi)/(2)\cdot10.5 \\ =16.493 \end{gathered}

So answer of C part is 16.493 meters.

User Hikaru
by
4.6k points