The formula for the surface area of a cylinder is given:
[tex]A=2\cdot\pi\cdot r\cdot h+2\cdot\pi\cdot r^2[/tex]
then, since the information given is a diameter, rewrite the expression using the diameter.
[tex]\begin{gathered} D=2\cdot r \\ r=\frac{D}{2} \\ \text{then, } \\ A=D\cdot\pi\cdot h+2\cdot\pi\cdot(\frac{D}{2})^2 \end{gathered}[/tex]
Replace with the data given
[tex]\begin{gathered} A=(2.5)\cdot(\pi)\cdot(16)+2\cdot\pi\cdot(\frac{2.5}{2})^2 \\ A=40\pi+3.125\pi \\ A=43.125\pi \end{gathered}[/tex]
