Explanation
We are given the following information:
[tex]\begin{gathered} Height\text{ }of\text{ }cylinder=9ft \\ Radius\text{ }of\text{ }circle=2ft \end{gathered}[/tex]We are required to determine the following:
• The lateral area.
,• Single base area.
,• Surface area.
The lateral area can be calculated as:
[tex]\begin{gathered} Lateral\text{ }Area=2\pi rh \\ Lateral\text{ }Area=2\times\frac{22}{7}\times2\times9 \\ Lateral\text{ }Area=\frac{792}{7}=113.14\text{ }ft^2 \end{gathered}[/tex]Hence, the lateral area is 113.14 ft².
The single base can be calculated as:
[tex]\begin{gathered} Area=\pi r^2 \\ Area=\frac{22}{7}\times2^2 \\ Area=\frac{88}{7}=12.57\text{ }ft^2 \end{gathered}[/tex]Hence, the single base area is 12.57 ft².
Therefore, the surface area can be calculated as:
[tex]\begin{gathered} Surface\text{ }area=lateral\text{ }area+top\text{ }area+base\text{ }area \\ Surface\text{ }area=113.14+12.57+12.57 \\ Surface\text{ }area=138.28\text{ }ft^2 \end{gathered}[/tex]Hence, the surface area is 138.28 ft².