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:
[tex]\begin{gathered} r=12+6 \\ \\ =18 \end{gathered}[/tex]
So overall area is (area of a circle)
[tex]\begin{gathered} A=\pi r^2 \\ \\ A=\pi(18)^2 \\ \\ A=324\pi \end{gathered}[/tex]
Radius of pool = 12
So the area of the pool is:
[tex]\begin{gathered} A=\pi r^2 \\ \\ A=\pi(12)^2 \\ \\ A=144\pi \end{gathered}[/tex]
So the path area is:
[tex]\begin{gathered} \text{ Path area = Overall area - pool area} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{ Path area = 324}\pi-144\pi \\ \\ =180\pi \end{gathered}[/tex]
If the one-gallon coating covered 7 then
[tex]\begin{gathered} \text{ coating amount = }\frac{180\pi}{7} \\ \\ =\frac{565.4866}{7} \\ \\ =80.78 \end{gathered}[/tex]
So 81 gallons of coating need.
