ANSWER
[tex]T.S.A = 150\pi[/tex] square inches.
EXPLANATION
The total surface area of a cylinder is given by;
[tex]T.S.A = 2\pi \: r(r + h)[/tex]
The height of the cylinder is , h=10in.
The radius of the cylinder is, r=5in.
We substitute the known values into the formula to obtain;
[tex]T.S.A = 2\pi \times 5(5+ 10)[/tex]
[tex]T.S.A = 10\pi(15)[/tex]
In terms of π, the total surface area is
[tex]T.S.A = 150\pi in^2[/tex]
