Who invented the volume of a pyramid

The volume of any pyramid is always one-third of the volume of a prism where the bases of the prism and pyramid are congruent and the heights of the pyramid and prism are also the same.

We can understand this by the following activity. Take a rectangular pyramid full of sand and take an empty rectangular prism whose base and height are as same as that of the pyramid. Pour the sand from the pyramid into the prism, we can see that the prism is exactly one-third full. In the same way, we can see that in a cube , there are three square pyramids arranged invisibly. Let us consider a pyramid and prism each of which has a base area 'B' and height 'h'. We know that the volume of a prism is obtained by multiplying its base by its height.

In the earlier section, we have seen that the volume of pyramid is one-third of the volume of the corresponding prism i. We can use this while solving the problems of finding the volume of the pyramid given its slant height. Thus, to calculate the volume of a pyramid, we can use the areas of polygons formulas as we know that the base of a pyramid is a polygon to calculate the area of the base, and then by simply applying the above formula, we can calculate the area of the base.

Here, you can see the volume formulas of different types of pyramids such as the triangular pyramid , square pyramid , rectangular pyramid , pentagonal pyramid, and hexagonal pyramid and how they are derived. Example 1: Cheops pyramid in Egypt has a base measuring about ft. Calculate its volume. Cheops Pyramid is a square pyramid. Its base area area of square is,. Answer: The volume of the Cheops pyramid is 91,, cubic feet.

Example 2: A pyramid has a regular hexagon of side length 6 cm and height 9 cm. Find its volume. Answer: The volume of the pyramid is Example 3: Tim built a rectangular tent that is of the shape of a rectangular pyramid for his night camp. What is the volume of the tent? The volume of a pyramid is the space that the pyramid occupies. Consider a square pyramid whose base is a square of length 'x'. From the diagram below it should be evident that the volume of the pyramid is less than one-half of the volume of the box that contains it.

It may be possible for the reader to see that the pyramid occupies over one-quarter of the box, hence its volume lies between one-quarter and one-half of the box in which it is contained. What Eudoxus found, using the calculus, is that any pyramid will occupy precisely one-third of the prism that contains it. Proof Consider any pyramid, perpendicular height h and with area of base A.

Imagine that the pyramid is split into n layers. Clearly the more layers, i. So it has been demonstrated that the volume of any pyramid is one-third the volume of the prism that contains it.