Volume of Pyramids

Concept

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.

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.

Rules

1. Determine the shape of the base of the pyramid and find the area of the base (B).
2. Determine the height (h) of the pyramid.
3. Use the formula V = $\fn_phv \frac{1}{3}Bh$ to calculate the volume of the pyramid.
4. State the volume in the appropriate cubic units.

Example

Find the volume of the pyramid.

Solution

V = $\fn_phv \frac{1}{3} \times base\;area \times height$

V = $\fn_phv \frac{1}{3}\times (\frac{1}{2}\times6.1\;m\times4.2\;m)\times (7.3\;m)$

V = 31.171 m³ or 31.2 m³

Practice Volume of Pyramids

Practice Problem 1

Find the volume of the pyramid.

Practice Problem 2

Find the volume of the pyramid. Round your answer to the nearest tenth.

Practice Problem 3

Sam is looking for the best deal for the sugar. Which product should he buy?

Practice Problem 4

Eve wants to fill a glass jar with decorative marbles. The glass jar is in the shape of a square-based pyramid, as shown below. What is the volume of Eve’s glass? Round your answer to the nearest tenth.