The sides of a square field are
12 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth.
THANK YOU!
First, get the area of the square field. The area of the square is side multiplied by side.
A = S x S
A = 12 X 12
A = 144 meters squared
Second, get the area of the circle formed by the sprinkler.
The circle is formed inside the square with a radius of 6 meters (half of the diameter which is 12 meters).
A = \pir^{2}
A = 3.14 x 6^2
A = 113.04 meters squared.
In order to get the not sprinkled area, subtract the area of the square by the area of the circle.
Not Sprinkled Area = 144 meters squared - 113.04 meters squared
the final answer is 30.96 meters squared
This is my 7th grade hw and I get it now
30.96 is the answer :P
I’m in 6th grade and I’m in enriched math so I had thins question so now I get it
Daes
so, what's the difference between the area of a 12x12 square and a circle of diameter 12?
To find the area that is not reached by the sprinkler, we need to first calculate the area of the square field and the area covered by the sprinkler. Then we can subtract the latter from the former.
The area of the square field can be calculated by squaring the length of one side:
Area of square field = (side length)^2 = 12^2 = 144 square meters
The diameter of the circular area covered by the sprinkler is equal to the length of one side of the square field. Since the radius of the circle is half of the diameter, the radius of the sprinkler's coverage is:
Radius = (side length) / 2 = 12 / 2 = 6 meters
To find the area of the circular region covered by the sprinkler, we can use the formula for the area of a circle:
Area of circle = π * (radius)^2 = π * 6^2 = 36π square meters
Now we can calculate the area of the field that is not reached by the sprinkler by subtracting the area covered by the sprinkler from the area of the square field:
Area not reached = Area of square field - Area of circle = 144 - 36π square meters
To round the answer to the nearest hundredth, we need to compute the numeric value of π and perform the subtraction:
Area not reached ≈ 144 - 36 * 3.14 square meters ≈ 144 - 113.04 square meters ≈ 30.96 square meters
Therefore, approximately 30.96 square meters of the field are not reached by the sprinkler.