Question

The irrigation system for a farm sprays water in circular patterns. Each sprinkler is connected to a pipe in the center of a circle and rotates around that pipe. The largest sprinkler sprays water 20 feet. What is the circumference of the circle irrigated by this sprinkler?

Answer 1

Here the irrigation sprinkler is pivoted at an angle
θ
=
40
∘
=
40
π
180
rad.
It waters a circular sector of area
A
=
2060
f
t
2
.
If the length of the sprinkler be
L
ft. It will be radius of the circular sector watered.
Hence
1
2
×
θ
in radian
×
L
2
=
A
⇒
L
=
√
2
A
θ
=
√
2
⋅
2060
⋅
180
40
π
≈
76.8
ft

Answer 2

40 π ft or 125.6ft

Explanation:

If the sprinkler can spray water 20 ft, that means the radius is 20 ft and to get the circumference we do 2 r π

or 2r*3.14

The answer is either 40 π ft

or 125.6ft