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| Math Central | Quandaries & Queries |
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rohan, a student: A CYLINDER IS WITHIN THE CUBE TOUCHING ALL THE VERTICALS FACES . A CONE IS INSIDE THE CYLINDER.IF THEIR HEIGHT ARE SAME WITH SAME BASE ,FIND THE RATIO OF THEIR VOLUMES. |
Hi Rohan,
Consider what the objects look like together:
Since the bases of the cylinder and the cone both have diameters of s (the length of one side of the cube), each of their radii is s/2. Both also have a height of s.
The formula for volume of a cylinder is
V = πr2h
The formula for volume of a cone is
V = πr2h/3
If you substitute in the radius and height for both, what is the ratio of their volumes?
Hope this helps,
Janice
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