The sides of a square field are 32 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. Use 3.14 for π.
the real answer is 220.16 m squared. that's the only way most homework websites will take the answer.
total area = 32 * 32 = A
sprinkled area = pi d^2/4 = pi (32*32)/4
difference= (32*32)(1-pi/4)
= 32*32 (1 - 3.14/4)
= 32*32 (.215)
we lose about 21.5 % of our grass seed :)
1024-803.8 = Area not covered.
220
The answer is actually 123.85 I learned that the hard way and yeah I tried 220.16 but it was corrected to 123.85 so yeahhhh so not make the same mistake i did.
To find out how much of the field is not reached by the sprinkler, we first need to calculate the area of the square field and the area covered by the sprinkler.
The formula to find the area of a square is side * side.
In this case, the sides of the square field are 32 meters, so the area of the field is 32 * 32 = 1024 square meters.
The sprinkler sprays a circular area with a diameter that corresponds to a side of the field. Since the sides of the field and the diameter of the circular area are the same, the diameter of the circular area is 32 meters.
The formula to find the area of a circle is π * (radius * radius), where π is approximately 3.14.
To find the radius of the circular area, we can divide the diameter by 2: 32 / 2 = 16 meters.
Now we can calculate the area of the circular area covered by the sprinkler: 3.14 * (16 * 16) = 3.14 * 256 ≈ 803.84 square meters.
To find the amount of the field not reached by the sprinkler, we subtract the area covered by the sprinkler from the total area of the field: 1024 - 803.84 ≈ 220.16 square meters.
Therefore, approximately 220.16 square meters of the field are not reached by the sprinkler.
As = 32^2 = 1024 m^2.
Ac = pi*r^2 = 3.14 * 16^2 = 803.8 m^2.
As-Ac = 1024 - 80j.8 = Area not reached.