The cylinder: Surface area and volume

Example

Calculate the area and volume of a cylinder with radius of the basis $3m$ and height $5m$.

The area of the basis will be:$$A_{basis}=2\cdot \pi \cdot r^2=18\pi$$ For the area or the side it is interesting to open the side face in order to get the shape of a rectangle and to see that one side is the height of the cylinder and the other the perimeter of the basis.

$$\begin{gathered} A_{lateral}=2\pi \cdot r\cdot h=30\pi \\ {A}_{total}=48\pi \end{gathered}$$

The volume will have the following expression:$$\begin{gathered} V=\pi \cdot r^2\cdot h \\ V=45\pi m^3 \end{gathered}$$