Question

The volume of a cylinder is calculated by multiplying the area of the base and the height. The volumes of a cylinder and a cone with the same radius and height are shown.

Which describes how to find the volume of a cone?​

Answer 1

Volume of a cone = ⅓volume of a cylinder

Answer 2

So the correct answer from the provided options would be:

"Multiply the area of the base and the height. Then multiply by
`\( (1)/(3) \)`."

To find the volume of a cone, you use the formula:

`\[ \text{Volume} = (1)/(3) \pi r^2 h \]`

where r is the radius of the base of the cone and h is the height of the cone.

The given options seem to be describing different approaches to finding the volume of a cone. The correct method is:

- Divide the area of the base by 3, then multiply by the height.

This is because the area of the base (which is a circle in the case of a cone) is
`\( \pi r^2 \)`, and then you multiply this area by the height of the cone and divide by 3, as shown in the volume formula above.

The volume of a cylinder (which is like a cone without the point, or a cone with a top) is given by the area of the base times the height, without dividing by 3:

`\[ \text{Volume of a cylinder} = \pi r^2 h \]`

The volume of a cone is exactly one-third the volume of a cylinder with the same base and height, which is why we divide by 3.