Describe an informal argument for the volume of a cone. If you know the volume of a cylinder, what must you do to find the volume of a cone that has the same height and base radius? (1 point)

Question

O You need to multiply the volume of the cylinder by 3.
You need to multiply the volume of
O the cylinder by 1/3.
You need to add 3 cubic units to the volume of the cylinder.
O You need to divide the volume of the cylinder by1/3

Answer 1

To understand the volume of a cone, let's first consider a cylinder that has the same height and base radius as the cone. The volume of a cylinder is calculated using the formula \( V = \pi r^2 h \), where \( r \) is the radius of the base, and \( h \) is the height.

Now, when we look at a cone with the same base and height, we can think of how the cone fits into the cylinder. The cone occupies only a portion of the space that the cylinder does.

An informal way to argue this is by visualizing the cone as being part of the cylinder. If we were to fill the cylinder with water, the cone would hold only a third of that water when both shapes have the same dimensions. This suggests that the volume of the cone is smaller than that of the cylinder.

In fact, through some geometric reasoning and experimentation, it has been found that the volume of a cone is exactly one-third of the volume of the cylinder with the same base and height. Therefore, to find the volume of the cone, you need to multiply the volume of the cylinder by \( \frac{1}{3} \).

So, the correct answer is: You need to multiply the volume of the cylinder by \( \frac{1}{3} \).