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

Question

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.

in progress 0
Evelyn 3 weeks 2021-09-26T16:17:54+00:00 1 Answer 0

Answers ( )

    0
    2021-09-26T16:19:30+00:00

    Answer:

    30.86 m^{2}

    Step-by-step explanation:

    Given:

    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.

    Question asked:

    How much of the field is not reached by the sprinkler ?

    Solution:

    First of all find the area of the square field.

    Area of the square field = (side)^{2}

                                            =12^{2} = 144 m^{2}

    As given diameter is corresponds to a side of the field diameter of circular area is 12,

    r = \frac{d}{2}  = \frac{12}{2} = 6 \ m

    Area of circle = \pi r^{2}

                          = \frac{22}{7} \times6\times6

                          = \frac{792}{7} = 113.142 \ m^{2}

    Now, in order to find that how much of the field is not reached by the sprinkler, we will subtract the circular area formed through spray from the total area of square field,

    144 – 113.142 = 30.858 m^{2}

    Therefore, 30.86 m^{2} of the field is not reached by the sprinkler.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )