Question

In the figure below, Ken's company has placed sprinkler heads at the center of the two small semicircles. The radius

Of the sprinklers is 5ft If the area in the larger semicircular area is the shape of the entire lawn, how much of the lawn will not be watered?

Answer 1

The answer is below

Explanation:

The sprinklers have a radius of 5 ft each. Since the larger semicircle (entire lawn) has a diameter that is formed from the 2 semicircles, therefore the radius of the larger semicircle is 10 ft.

Area that wont be watered can be gotten by subtracting the area of the two smaller circles from the area of larger semicircle.

Area that wont be watered = 1/2(π * 10²) - 2[1/2(π * 5²)] = 50π - 25π = 25π ft²