To find the volume of a cone that has the same height and base radius as a cylinder, you can use an informal argument based on the relationship between the two shapes.
A cone can be thought of as a pyramid with a circular base, and it occupies a part of the space that a cylinder does. In fact, if you look at the geometry, it turns out that a cone takes up exactly one-third of the volume of a cylinder that has the same base radius and height.
So, if you already know the volume of the cylinder (which is calculated using the formula \( V = \pi r^2 h \)), to get the volume of the cone, you need to take the volume of the cylinder and divide it by 3.
Thus, the correct response is: You need to divide the volume of the cylinder by \( \frac{1}{3} \) (which is the same as multiplying the volume of the cylinder by \( \frac{1}{3} \)).
In summary:
- To find the volume of the cone, divide the volume of the cylinder by 3.