Question

Each of 3 water sprinkler systems covers a semicircle with radius 2m on the

side of a house shown.

What amount of area remains dry? Show your work to explain how you go

your answer, to the nearest square meter. (Dry area is in the shaded

region.)

Answer 1

5 meters

Explanation:

We can obtain the entire area, both shaded and non-shaded by finding the area of the rectangle ;

Area of rectangle = Length * width

Length = 12 ; width = 2

Area of rectangle = 12 * 2 = 24 m²

Area of semicircle = πr² / 2

The radius, r of each semicircle = 2

Area of each semicircle = π * 2² / 2 = 6.283 m²

Area of the 3 semicircles = 3 * 6.283 = 18.849 m²

Area of dry region:

(24 - 18.849) m²

= 5.151 m²

= 5 m