Question

The sides of a square field are 16 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.

Answer 1

16 divided by
`\pi`=answer

Answer 2

The answer is 55.04 square meters.

Explanation:

The sides of a square field are 16 meters.

A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field.

So, we can say that the maximum circle that can be in the square will have the diameter of 16 meters.

That gives the radius as = 8 meters

Area of the square is =
`16*16=256` square meters

Now, area of the circle =
`\pi r^(2)` =
`3.14*8*8=200.96` square meters

So, the area that the sprinkler does not cover is

`256-200.96=55.04`square meters.