6th grade Q4

How do you determine the relationship of the volume between a rectangular prism and a pyramid?

How do you determine the relationship of the volume between a cylinder and a cone?

The volume of a cone is exactly one third the volume of a cylinder with the same base radius and height.

Here's the math behind it:

Volume of a Cylinder:

V_{cy l in d er} = π r^{2} h

where $r$ is the radius of the base of the cylinder, and $h$ is the height.

Volume of a Cone:

V_{co n e} = \frac{1}{3} π r^{2} h

This formula also uses the same radius $r$ and height $h$ .

So, if you compare these two:

This means that the volume of the cone is one third that of the cylinder when both shapes have the same base and height.

V_{co n e} = \frac{1}{3} V_{cy l in d er}

This relationship can be visualized by imagining filling a cone with water and pouring it into a cylinder of the same dimensions; it would take exactly three cones of water to fill the cylinder completely.

Example:

If a cylinder has the volume of 30 cubic units, the cone with the same base and height has the volume of 10 cubic units.