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FutureStarrA The volume of a Pyramid
A pyramid is a three-dimensional shape with a triangular base and a square top. It represents the distribution of goods among a group of people. The shape’s basic appearance is that of a triangle.
The volume of pyramid is space occupied by it (or) it is defined as the number of unit cubes that can be fit into it. A pyramid is a polyhedron as its faces are made up of polygons. There are different types of pyramids such as a triangular pyramid, square pyramid, rectangular pyramid, pentagonal pyramid, etc that are named after their base, i.e., if the base of a pyramid is a square, it is called a square pyramid. All the side faces of a pyramid are triangles where one side of each triangle merges with a side of the base. Let us explore more about the volume of pyramid along with its formula, proof, and a few solved examples.
The volume of a pyramid refers to the space enclosed between its faces. 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, i.e., three identical pyramids of any type can be arranged to form a prism of the same type such that the heights of the pyramid and the prism are the same and their bases are congruent, i.e., three rectangular pyramids can be arranged to form a rectangular prism. 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. (Source: From the earlier section, we have learned that the volume of a pyramid is (1/3) × (area of the base) × (height of the pyramid). 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 volume of pyramid. 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. (Source: www.cuemath.com)