Question

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

Answer 1

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.