1. Sphere Volume (V_sphere):
The formula for the volume of a sphere is given by:
2. Cylinder Volume (V_cylinder):
The volume of a cylinder is given by:
Since h = 2r, we substitute to get:
3. Cone Volume (V_cone):
The volume of a cone is one third of the volume of a cylinder with the same base and height:
Since h = 2r, we substitute to get:
Now, let's compare these formulas:
- The sphere's volume is
- The cylinder's volume is
- The cone's volume is
So the volumes relate to each other like this:
- The cylinder's volume is 3 times the cone's volume.
- The sphere's volume is 2 times the cone's volume.
- The cylinder's volume is 1.5 times the sphere's volume.
Putting these relationships together:
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