Question

A cone fits inside a square pyramid as shown. For

Answer 1

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

∗

=