Question

1. calculate the area of the lawn covered by an oscillating sprinkler that sprays water in a half - circle with a radius of 10 ft.

Explanation:

Step1: Recall area formula for circle

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

Step2: Calculate area of half - circle

Since the sprinkler sprays water in a half - circle, the area of the half - circle $A_{half}$ is half of the area of a full - circle. So $A_{half}=\frac{1}{2}\pi r^{2}$. Given $r = 10$ ft, we substitute $r$ into the formula: $A_{half}=\frac{1}{2}\pi\times(10)^{2}=\frac{1}{2}\pi\times100 = 50\pi$ square feet.

Answer:

$50\pi$ square feet