To calculate the surface area of a cilinder, we have to calculate the lateral area and the area of the circles at the bottom and at the top of the cilinder.
We can calculate the lateral area of the cilinder, with the following formula: 2 x Pi X r X h
Being, r the radius and h the height.
[tex]\begin{gathered} \text{Lateral area= 2}\cdot\pi\cdot7\cdot6 \\ \text{Lateral area= 263.89 cm}^2 \end{gathered}[/tex]
Now we calculate the area of the circle, both circles have the same measures so we would just have to multiply the area of the circle by two.
[tex]\begin{gathered} \text{Area circles= }2\cdot\pi\cdot r^2 \\ \text{Area circles= 2}\cdot\pi\cdot7^2=307.87cm^2 \end{gathered}[/tex]
Then to have the total surface area, we add both areas lateral area and the area of the circles.
Total surface area = Lateral area + area of both circles
[tex]\begin{gathered} \text{Total surface area= 263.89 + 307.87} \\ \text{Total surface area = 571.76}\approx572\operatorname{cm} \end{gathered}[/tex]
