Cones and Spheres - Volume
Complete the steps in order:
1. Find the volume of the cube in terms of the side length x.
2. Think about how you might split the cube into 3 pyramids.
3. Click the "Show Pyramids" box. Did you split the cube in the same way?
4. Click the "Show Object Volumes" box to see the actual volumes for the case when x = 1.
5. Click the "Animate" button to see how the pyramids and the cube line up.
6. How would the result change if we altered the height of the cube to some number h?
Complete the steps in order:
1. Find the area of the cross sections of the pyramid and cone displayed on the right in terms of the dimensions provided.
2. Look up Cavalieri's Principle
3. Use what you learned from the first applet together with Cavalieri's Principle to derive the volume of the cone in terms of the volume of the pyramid using the given dimensions.
Complete the steps in order:
1. Find the areas of the annular cross section of the plane through the cylinder and cone, and the area of the circular cross sections of the sphere.
2. Use Cavalieri's Principle to make to determine the volume of the sphere in terms of the given radius r.
3. Check the boxes and compare the areas and volumes shown. Are they consistent with your previous conclusions?