the height of an oil tank (cylinder) is 13 yards and the diameter of its base measures 6 yards. calculate the tanks total surface area

The total surface area   is given by :

2 * pi * ( base diameter / 2)^2   +  2 * pi * (base diameter/ 2) (height)  =

2 * pi * ( 6 / 2)^2   +  2 * pi * (6/ 2) (13)  =

2 * pi (3)^2  + 2 * pi * (3)(13)   =

2 * pi  [ 9 + 39]  =

2 * pi  [ 48 ]  =

96 pi   square  yards  ≈   301.6  square yards

Another possibility..... Most of the oil tanks I see around here in oil country sit on the ground....so if you had to paint the entire surface area, you would paint the side(s) and the top....

Top = pi x r^2 = pi x 3^2 = 28.274 m^2

The side(s) = pi x d x h = 245.044

Total=273.32 m^2