a sprinkler is placed in the corner of a rectangular yard,if the sprinkler has a of reach 26 feet and the yard is 30 feet long and 40 feet wide how many square feet of the lawn will not be watered by the sprinkler? 30ft-26ft = 4ft, 40ft-26ft=14
14ft * 4ft = 56ft....?
I will assume that the sprinkler is a circular one, although some like the sweeping kind, are not.
area of rectangle = 30x40 or 1200 ft^2
the area covered by the sprinkler is 1/4 of a circle with radius 26
area of watered lawn = (1/4)π(26)^ = 169π
so area not covered by sprinkler = (1200 - 169π) ft^2
To solve this problem, we need to determine the area of the rectangular yard that will not be watered by the sprinkler.
Given:
Length of the yard = 30 feet
Width of the yard = 40 feet
Radius of the sprinkler's reach = 26 feet
To find the area of the lawn that will not be watered by the sprinkler, we first need to calculate the distance from the sprinkler to each side of the yard.
- Distance from the sprinkler to the left side: This is equal to the width of the yard minus the radius of the sprinkler's reach: 40 ft - 26 ft = 14 ft.
- Distance from the sprinkler to the right side: This is also equal to 14 ft since the yard is rectangular and the sprinkler is placed at the corner.
- Distance from the sprinkler to the top side: This is equal to the length of the yard minus the radius of the sprinkler's reach: 30 ft - 26 ft = 4 ft.
- Distance from the sprinkler to the bottom side: This is also equal to 4 ft since the yard is rectangular and the sprinkler is placed at the corner.
Now, we can calculate the area of the lawn that will not be watered. This can be done by multiplying the distances on the top and bottom sides by the distances on the left and right sides:
Area = (Distance on the top side + Distance on the bottom side) * (Distance on the left side + Distance on the right side)
Area = (4 ft + 4 ft) * (14 ft + 14 ft)
Area = 8 ft * 28 ft
Area = 224 square feet
Therefore, 224 square feet of the lawn will not be watered by the sprinkler.