# Thread: Designing a Water Sprinkler

1. ## Designing a Water Sprinkler

An engineer is asked to design a water sprinkler that will cover a field of 100 square yards that is in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler rotate?

2. Hello, magentarita!

An engineer is asked to design a water sprinkler that will cover a field
of 100 square yards that is in the shape of a sector of a circle of radius 50 yards.
Through what angle should the sprinkler rotate?

We are expected to know the area formula for a sector of a circle: . $A \:=\:\tfrac{1}{2}r^2\theta$ .[1]

. . where $r$ is the radius and $\theta$ is the central angle in radians.

We know: . $A = 100,\;r = 50$

Substitute into [1]: . $100 \:=\:\tfrac{1}{2}(50^2)\theta$

Therefore: . $\theta \;=\;0.08\text{ radians} \;\approx\;4.58^o$

3. ## wow....

Originally Posted by Soroban
Hello, magentarita!

We are expected to know the area formula for a sector of a circle: . $A \:=\:\tfrac{1}{2}r^2\theta$ .[1]

. . where $r$ is the radius and $\theta$ is the central angle in radians.

We know: . $A = 100,\;r = 50$

Substitute into [1]: . $100 \:=\:\tfrac{1}{2}(50^2)\theta$

Therefore: . $\theta \;=\;0.08\text{ radians} \;\approx\;4.58^o$
I had no idea it was that simple.

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