Chapter 12.4, Problem 47HP

To determine

To explain:

The formulas for the volume of a prism and the volume of a cylinder is similar.

Answer to Problem 47HP

Two separate formulas for the volume of a prism and volume of a cylinder only because a cylinder is not a prism. Otherwise their volumes works for both.

Explanation of Solution

Given information:

The formulas for the volume of a prism and the volume of a cylinder is similar.

Volume of a cylinder is:

  $V=\pi r^{2}h$

And volume of a prims is:

  $V=Bh$ , where $B$ is the area of the base which is in the form of circle.

So, the base area is:

  $B=\pi r^2$

Now, substitute $B=\pi r^2$ in the formula of volume of prism then it is look similar to the volume of the cylinder as follows:

  $\begin{array}{c}V=Bh\\ =\pi r^{2}h\end{array}$

So, they are similar.

They are different because a cylinder is not a prism.