Question

page 16 of 16 Volume of a Cone Quick Check 1 of 51 of 5 Items Question 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) 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 3. You need to multiply the volume of the cylinder by 3. 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 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 . Skip to navigation

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 \(\frac{1}{3}\). This means that the volume of the cone is one-third the volume of the cylinder.

The reasoning behind this is that a cone can be thought of as a pyramid with a circular base, and it has been shown through informal arguments (such as comparing the volume of a cone with that of a cylinder) that the cone occupies one-third the space of the cylinder when they share the same height and base area.

So, the correct response is:

**You need to multiply the volume of the cylinder by \(\frac{1}{3}\).**