Example 2
Find the dimensions for a cone that has the same volume as a pyramid of the same height as the cone. Both the cone and the pyramid have a height of meters. The volume of the pyramid is cubic meters. A cone and a pyramid both taper to a point or vertex at the top. The “slant” of the taper is linear, meaning it is a straight line. The dimensions of both the cone and the pyramid change at a constant rate from base to tip.
- Cavalieri’s Principle states that the pyramid and cone will have the same volume if the area of each cross section of a plane is the same at every height of the two objects. This means that if the cone and pyramid have bases of equal area, then their volumes will also be equal.
- Set up an equation to find the radius of the cone.