Question

The irrigation design for a new backyard is shown with four sprinkler heads and two walkways.

The distance between grid lines is 3 feet.


Which statements about the design are true? Check all that apply.

Each sprinkler head is placed more than 3 feet from the walkway.

If two additional sprinkler heads are placed on the lawn, every square foot of the yard would be watered.

The total area watered by each sprinkler is approximately 63.6 square feet.

The total area watered by all the sprinklers is approximately 254 square feet.

If the sprinklers were placed in two straight lines on the yard, they would water a greater amount of the lawn.

Answer 1

Each sprinkler head is placed more than 3 feet from the walkway; The total area watered by each sprinkler is approximately 63.6 square feet; The total area watered by all the sprinklers is approximately 254 square feet.

Explanation:

The head of each sprinkler is more than one grid box away from the walkway. Since each grid is 3 feet, this means each sprinkler head is placed more than 3 feet from the walkway.

The distance from the sprinkler head to the edge of the circle watered is 1.5 boxes. Since each box is 3 feet, this makes the radius of each circle 3(1.5) = 4.5 feet.

This means the area of each circle would be

A = 3.15(4.5)^2 = 63.585 ≈ 63.6 ft².

This also means that the four sprinklers together water 63.6(4) = 254.4 ≈ 254 ft².

Answer 2

Statements A, C, D are true

Explanation:

A). As we can see distance from the sprinklers head to the walkway is more than one grid and length of one grid is 3 feet, so each sprinkler is placed more than 3 feet from the walkaway.

B). If two additional sprinkler heads are placed on the lawn, every square foot of the yard would be watered is not certain because the position of additional sprinklers is not defined.

C). Radius of the area watered by each sprinkler = 1.5 grid = 1.5×3 = 4.5 feet

So area watered by each sprinkler = π×r² = (3.14)(4.5)² = 63.58 ≈ 63.6 feet²

D). Area watered by one sprinkler = 63.6 feet²

therefore total area covered by four sprinklers = 4×63.6 = 254 feet²

E). If the sprinklers are placed in two straight lines on the yard then area watered by them will be same. No additional area will be watered by them.