A lawn sprinkler sprays water 78.5 square feet area and sprays in every direction as it rotates. What is the length of the sprinkler’s stream of water?
To find the length of the sprinkler's stream of water, we need to calculate the radius of the area covered by the sprinkler.
Given that the sprinkler sprays water in a 78.5 square feet area, the area covered by the sprinkler can be considered as a circle.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Given the area is 78.5 square feet, we can substitute this into the formula:
78.5 = πr^2
Now, we can solve for the radius:
r^2 = 78.5 / π
r^2 ≈ 24.9662
r ≈ √24.9662
r ≈ 5 feet
The length of the sprinkler's stream of water is equal to the circumference of the circle, which is given by the formula C = 2πr. Therefore:
C = 2π(5)
C ≈ 31.42 feet
Therefore, the length of the sprinkler's stream of water is approximately 31.42 feet.