# The cylinder: Surface area and volume

The cylinder is the surface with two circular bases joined by one side, as shown below:

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

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.

$$A_{lateral}=2 \pi \cdot r \cdot h =30 \pi \\A_{total}=48\pi$$

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