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 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 .

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 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.

Answer 1

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.