Question

Prove that cone is 1/3of the cylinder

Answer 1

Answer:

Step-by-step explanation:

We just need the base of the square pyramid to have side length. Such a pyramid has volume 1/3⋅h⋅π⋅r^2.

Then the area of the base is clearly the same. The cross-sectional area at distance a from the peak is a simple matter of similar triangles: The radius of the cone's cross section will be a/h×r. The side length of the square pyramid's cross section will be a h⋅rπ

Once again, we see that the areas must be equal. So by Cavalieri's principle, the cone and square pyramid must have the same volume:1/3⋅h⋅π⋅r^2