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Hello I'm working on some homework questions and need help thanks

Hello I'm working on some homework questions and need help thanks-example-1
User Georstef
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1 Answer

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Given:

The radius of the inner circle = 12 yd

Width of the path = 6

One gallon of coating covered = 7

Find-: How many gallons of coating need.

Sol:

The radius of the path is:


\begin{gathered} r=12+6 \\ \\ =18 \end{gathered}

So overall area is (area of a circle)


\begin{gathered} A=\pi r^2 \\ \\ A=\pi(18)^2 \\ \\ A=324\pi \end{gathered}

Radius of pool = 12

So the area of the pool is:


\begin{gathered} A=\pi r^2 \\ \\ A=\pi(12)^2 \\ \\ A=144\pi \end{gathered}

So the path area is:


\begin{gathered} \text{ Path area = Overall area - pool area} \\ \end{gathered}
\begin{gathered} \text{ Path area = 324}\pi-144\pi \\ \\ =180\pi \end{gathered}

If the one-gallon coating covered 7 then


\begin{gathered} \text{ coating amount = }(180\pi)/(7) \\ \\ =(565.4866)/(7) \\ \\ =80.78 \end{gathered}

So 81 gallons of coating need.

User Johnbot
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