ANSWER
15 square inches
EXPLANATION
From the given question,
[tex]\text{height h =}3\frac{5}{8}=3.625[/tex]
and the diameter d is
[tex]\begin{gathered} d=2\frac{1}{2}=2.5 \\ r=1.25\text{ } \end{gathered}[/tex]
The formula for finding the lateral surface area is :
[tex]\begin{gathered} A_l=\pi rl \\ l=\sqrt[]{r^2+h^2} \\ \end{gathered}[/tex]
solving for
[tex]\begin{gathered} A_l \\ A_l=\pi r\sqrt[]{r^2+h^2} \\ =\pi\times1.25\sqrt[]{3.63^2+1.25^2} \\ =15.05791 \\ =15 \end{gathered}[/tex]
The answer is 15 to the nearest square inches
