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

Responses

You need to add 3 cubic units to the volume of the cylinder.
You need to add 3 cubic units to the volume of the cylinder.

You need to multiply the volume of the cylinder by 13
.
You need to multiply the volume of the cylinder by Start Fraction 1 over 3 End Fraction .

You need to multiply the volume of the cylinder by 3.
You need to multiply the volume of the cylinder by 3.

You need to divide the volume of the cylinder by 13
.
You need to divide the volume of the cylinder by Start Fraction 1 over 3 End Fraction .

Answer 1

To informally argue for the volume of a cone, we can start by considering how a cone relates to a cylinder.

Imagine you have a cylinder with a specific height and base radius. The volume of a cylinder is calculated 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 take a cone that has the same height and base radius as this cylinder, the volume of the cone is different. An informal way to understand why the volume of the cone is less than the cylinder is to visualize how much space the cone occupies.

If you were to fill the cylinder with water and then try to fit the cone inside, you'd find that the cone only occupies part of the space of the cylinder. In fact, it can be visually estimated or reasoned that three cones could fill up one cylinder of the same height and base radius. Thus, the cone takes up one-third of the volume of the cylinder.

Therefore, if you know the volume of the cylinder, to find the volume of the cone with the same height and base radius, you must multiply the volume of the cylinder by \( \frac{1}{3} \).

So the correct response would be: You need to multiply the volume of the cylinder by \( \frac{1}{3} \).