To calculate the volume of a cylinder, we multiply the area of the base by the height.
Note that if the radius of the circular base of a cylinder is r, then the area of the base B is π r^2.
Let's substitute this area into the formula for the volume.
V = Bh ⇒ V=(π r^2)h
The result is a formula for the volume of a cylinder with a radius r and height h. Let's now remember the formula for the volume of a rectangular prism.
Volume of a Prism
Same as before, we calculate the volume by multiplying the area of the base by the height.
The only difference is that this time the base is a rectangle, not a circle. If l and w are the length and width of the base, the area of the base is l * w.
Let's then substitute this expression for B in the formula.
V = Bh ⇒ V= (l w) h
We can use this formula to find the volume of a prism with a rectangular base.
Comparison
See that the rules to calculating the volumes are the same. In both cases we multiply the area of the base B by the height of the figure h.
\begin{gathered}
V_\text{cylinder} = Bh \quad \text{ vs } \quad V_\text{prism} =Bh
\end{gathered}
The only difference are the areas of the bases. The base of a cylinder is a circle and the base of a rectangular prism is a rectangle. As a result, the final formulas are different.
\begin{gathered}
V_\text{cylinder} = \pi r^2 h \quad \text{ vs } \quad V_\text{prism} =\ell w h
\end{gathered}
