At the park there is a pool shaped like a circle with diameter 22 yd. A ring-shaped path goes around the pool. Its width is 6 yd. We a

Question

At the park there is a pool shaped like a circle with diameter 22 yd. A ring-shaped path goes around the pool. Its width is 6 yd.
We are going to give a new layer of coating to the path. If one gallon of coating can cover 5 yd”, how many gallons of coating do we need? Note that coating
comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for n).

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Anna 2 months 2021-10-20T22:13:35+00:00 1 Answer 0 views 0

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    2021-10-20T22:14:56+00:00

    Answer:

    106 gal

    Step-by-step explanation:

    step 1

    Find the area of the path

    we know that

    The area of the path is given by the formula

    A=\pi r_2^{2} -\pi r_1^{2}

    A=\pi [r_2^{2} -r_1^{2}]

    where

    r_2 is the radius of the pool plus the width of the path

    r_1 is the radius of the pool

    we have

    r_1=22/2=11\ yd —> the radius is half the diameter

    r_2=11+6=17\ yd

    substitute

    A=\pi [17^{2}-11^{2}]

    A=168\pi\ yd^2

    assume

    \pi =3.14

    A=168(3.14)=527.52\ yd^2

    step 2

    Find the gallons of coating needed

    Divide the area of the path by 5

    so

    527.52/5=105.5\ gal

    Round up

    therefore

    106 gal

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