To informally derive the volume of a cone, we can start by comparing it to a cylinder. Imagine a cylinder that has the same base radius and height as the cone. The volume \( V \) of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
where \( r \) is the radius of the base and \( h \) is the height.
Now, if you consider a cone that fits perfectly inside this cylinder, you'll notice that the cone occupies only a portion of the cylinder's volume. Through geometric reasoning or even experimentation (like filling the cone with a liquid and pouring it into the cylinder), you can see that it takes three cones to fill the cylinder completely.
This leads to the conclusion that the volume of the cone is one-third of the volume of the cylinder. Therefore, to find the volume of a cone with the same height and base radius as a cylinder, you need to divide the volume of the cylinder by 3.
Thus, the correct response is:
You need to multiply the volume of the cylinder by \( \frac{1}{3} \).