Answer:
Answer on Question #47534 – Math – Geometry
How to prove the volume formula of con is 1/3×π×r^2×h;without using
integration?
Solution.
Suppose we take a slice of the pyramid with the cone inside, from some way up
the pyramid. This will look like a square with a circle fitting inside. Radius of the
cone at this point, will be x.
The area of the circle is
The area of the square is × =
The ratio of the circle to the square is
.
The same is true for every slice we take: the area of the circle is
of the area
of the square.
So, the volume of the cone will be
the volume of the pyramid.
The pyramid's volume is
.
So the cone's volume is
∗
=
