Question

a sprinkler is placed at the center of the lawn. a sprinkler sprays water in a circular pattern as shown in the figure. what a square lawn has area 50 ft². what is the radius of the circle? the radius of the circle is □ ft. (simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Recall the area - formula of a circle

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius.

Step2: Solve for the radius

Given $A = 50$ square - feet, we have $50=\pi r^{2}$. Then $r^{2}=\frac{50}{\pi}$, and $r=\sqrt{\frac{50}{\pi}}$. Simplifying, $r = \sqrt{\frac{25\times2}{\pi}}=\frac{5\sqrt{2}}{\sqrt{\pi}}=\frac{5\sqrt{2\pi}}{\pi}$ feet.

Answer:

$\frac{5\sqrt{2\pi}}{\pi}$