Question

The irrigation design for a new backyard is shown with six sprinkler heads and two walkways. Which statement is true of this design? The area covered by each sprinkler head is approximately 113.10 ft2. The area covered by all the sprinkler heads together is approximately 169.64 ft2. Every square foot of the yard will be watered with this design. The sprinklers would cover more area if they were in a straight line.

Answer 1

Answer:B on edge

Step-by-step explanation:

Answer 2

Option third "The area covered by all the sprinkler heads together is approximately 169.64 ft2" is correct.

What is a circle?

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have:

The distance between grid lines is 2 ft

As we can see from the figure each sprinkler head consists of 3 grid squares.

It means the diameter of each sprinkler head = 3×2 = 6 ft

The radius is half of the diameter = 6/2 ⇒ 3 ft

We know the area of the circle is given by:

$\rm A = \pi r^2$

The area of each sprinkler head:

$\rm A = \pi \times 3^2$

A = 9π square ft  or

A = 28.2743 square ft

The total sprinkler head = 6

Now the total area covered by all the sprinkler heads together:

= 6×28.2743

= 169.64 square ft.

Thus, option third "The area covered by all the sprinkler heads together is approximately 169.64 ft2" is correct.

Learn more about circle here:

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