We calculate the volume by multiplying the base's area 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. We know this because this is the formula for the area of a circle.
Let's substitute this area into the formula.
V = Bh ⇒ V=π r^2h
Doing that results in a formula for the volume of a cylinder with a radius r. Great work so far. Now recall the formula for the volume of a rectangular prism.
Volume of a Prism
Same as before, we calculate the volume by multiplying the base's area by the height.
This time, the only difference is that 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 rectangle shaped base.
Similarities
See that the rules to calculating the volumes are the same. In both cases we multiply the area of the base by the height of the figure.
\begin{gathered}
V_\text{cylinder} = Bh \quad \text{ vs } \quad V_\text{prism} =Bh
\end{gathered}
The only difference lies in the areas of the base. 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.
