Question

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?

Answer 1

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.