Volume Of A Right Square Pyramid - Formula, Examples, Definition

Volume of a Right Square Pyramid

The volume of a right square pyramid is the space occupied by the right square pyramid. A right square pyramid is a three-dimensional geometric shape that has a right square base and four triangular faces that are joined at a vertex. Let's learn how to find the volume of a right square pyramid with the help of a few solved examples and practice questions.

1.	What is Volume of a Right Square Pyramid?
2.	Formula of Volume of a Right Square Pyramid
3.	How to Find the Volume of a Right Square Pyramid?
4.	FAQs on Right Square Pyramid Volume

What is Volume of a Right Square Pyramid?

The volume of a right square pyramid is the number of unit cubes that can fit into it. A right square pyramid is a three-dimensional shape that has a right square base and four triangular faces that are joined at a vertex. A right square pyramid is a polyhedron (pentahedron) with five faces. The unit of volume is "cubic units". For example, it can be expressed as m3, cm3, in3, etc depending upon the given units.

A right square pyramid has three components.

• The top point of the pyramid is called the apex.
• The bottom right square is called the base.
• The triangular sides are called faces.

Formula of Volume of a Right Square Pyramid

The formula to determine the volume of a right square pyramid is V = 1/3 × b2 × h where "b" is the length of the base and "h" is the perpendicular height. The relation between slant height, perpendicular height, and the base is given by using Pythagoras Theorem s2 = h2 + (b/2)2 where "s", "h" and "b" are slant height, the height of perpendicular, and base length of the right square pyramid, respectively. Thus, the volume of the right square pyramid is given by replacing the given dimensions in the formula V = 1/3 × b2 × h.

How to Find the Volume of a Right Square Pyramid?

As we learned in the previous section, the volume of a right square pyramid could be found using \(\dfrac{1}{3} \times \text{b}^2 \times \text{h}\). Thus, we follow the below steps to find the volume of a right square pyramid.

• Step 1: Determine the base area (b2) and the height (h) of the pyramid.
• Step 2: Find the volume using the formula 1/3 × b2 × h
• Step 3: Represent the final answer with cubic units.

Example: Find the volume of the right square pyramid having height and length of the base edge of 9 units and 5 units respectively.

Solution: Given that h = 9 units and b = 5 units.

Then, the volume of the right square pyramid is V = 1/3 × b2 × h ⇒ V = 1/3 × 52 × 9 ⇒ V = 52 × 3 = 75 cubic units

Answer: The volume of the right square pyramid is 75 cubic units.