To fidn the surface area of the grain tank you need to find the area of:
Cylinder (without one of the bases as there are just one base exposed), use the next formula:
[tex]A_1=\pi\cdot r^2+h(2\pi r)[/tex]
You have for the given cylinder:
h=12ft
r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft
[tex]\begin{gathered} A_1=\pi(4.2ft)^2+12ft(2\pi(\text{4}.2ft)) \\ =17.64\pi ft^2+100.8\pi ft^2 \\ =118.44\pi ft^2 \end{gathered}[/tex]
Cone (without the base as the base is not exposed), use the next formula:
[tex]A_2=\pi\cdot r\cdot s[/tex]
You have for the given cone:
r= 4.2ft
s= 5.5ft
[tex]\begin{gathered} A_2=\pi(4.2ft)(5.5ft) \\ =23.1\pi ft^2 \end{gathered}[/tex]
The entire exposed surface of the tank is:
[tex]\begin{gathered} A_T=118.44\pi ft^2+23.1\pi ft^2 \\ \\ =141.54\pi ft^2 \\ \\ \approx444.66ft^2 \end{gathered}[/tex]
The approximate amount of surface area that will receive the painting is 444.66 squared feets
