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.

Answer 1

To find the volume of a cone that has the same height and base radius as a cylinder, you need to multiply the volume of the cylinder by \(\frac{1}{3}\).

Here's an informal argument:

Imagine filling up a cylinder with water. If you were to fill it to the top, you would have a certain volume of water (the volume of the cylinder). Now, if you take a cone that fits perfectly inside that cylinder (with the same base and height), the cone will fill only a portion of that space.

Through experiments or visualizations, you can observe that three such cones can fit into that cylinder without any leftover space. This means the volume of the cone is one-third the volume of the cylinder.

Therefore, you can conclude that to find the volume of the cone, you take the volume of the cylinder and multiply it by \(\frac{1}{3}\).

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