Volume of a Square Pyramid

Volume is nothing but the space occupied by the object in 3-D and the volume of a square pyramid is the space occupied by the five faces of the square pyramid. A square pyramid is a three-dimensional geometric formed with a square base and four triangular side faces connected such that they all meet at the apex of the square pyramid.

The volume of the square pyramid is the volume of space enclosed inside all its five faces. Now let’s learn about the square pyramid, its volume, examples, and others in this article.

What is Volume of a Square Pyramid?

The volume of any solid is the total space occupied by all the faces of the solid. We know that a square pyramid has five faces one square face and four triangular faces, and the volume of a square pyramid is the total volume of material enclosed inside all these faces. We can easily get the volume of the square pyramid by easily taking the product of the area of the square base and the height of the pyramid and then dividing the result by 3. Thus, we define the volume of the square pyramid as,

Volume = (1/3) × (Base Area) × (Height)

The volume of a square pyramid is measured in cubic units and the generally used units are m³, cm³, etc.

What is a Square Pyramid?

We define the square pyramid as a 3-D object which has a square base and five triangular faces these faces are attached to each of the square base sides and then the faces are closed in such a manner that the top point of all the bases meets at the point on the top of the pyramid called the vertex of the square pyramid. A square pyramid has three parts that are,

• Apex of the Pyramid is the top point of the square pyramid.
• A Square Base
• Four Triangular Faces

The various examples of square pyramids are the Great Pyramid of Giza, decorative items, perfume or wine bottles, etc.

Volume of a Square Pyramid Formula

A square pyramid’s volume is defined as the space enclosed within its five faces. To calculate the volume, values of the base area and height of the square pyramid are needed. The formula for calculating the volume of a square pyramid is 1/3 times the product of the base area and the height of the square pyramid. The standard unit of measurement of volume is cubic meters (m³).

V = 1/3 × A × h

Where,

• V is the Volumeof Square Pyramid, 
• A is the base area of Square Pyramid, and
• h is the height of Square Pyramid.

We know that area of square base is b² where a is the side of the square base. Now the volume of the square pyramid formula becomes.

V = 1/3 × b² × h

How To Find the Volume of a Square Pyramid?

We can easily find the volume of the square pyramid by following the steps discussed below. 

Step 1: Note the dimensions of the square pyramid i.e. the side of the square base (b) and the height of the pyramid (h).

Step 2: Find the area of the square base using the formula, A = b² units²

Step 3: Now use the volume of the square pyramid formula and simplify to get the required volume i.e.,

Volume of Square Pyramid = 1/3×(A)(h)

Let’s take an example to understand the above steps in detail.

Example: Find the volume of a square pyramid of a square base of the length 8 m and height 6 m.

Solution:

Step 1: The dimensions of square pyramid are,

• Side of Square Base (a) = 8 m
• Height of Pyramid (h) = 6 m

Step 2: Area of Square Base,

A = a² = (8)² = 64 m²

Step 3: Using the formula,

Volume of Square Pyramid = 1/3×(A)(h)

⇒ V = 1/3×(64)(6)

⇒ V = 128 m³

The required volume of the square pyramid is 128 m³

Solved Examples on Volume of a Square Pyramid

Example 1: Find the volume of a square pyramid if the area of the base is 60 m² and the height of the square pyramid is 10 m.

Solution:

Given,

Area of Base (A) = 60 m²
Height (h) = 10 m

Using the Formula,

V = 1/3 × A × h

⇒ V = 1/3 × 60 × 10

⇒ V = 200 m³

Thus, the volume of the given square pyramid is, 200 m³

Example 2: Find the area of the base of the square pyramid if its volume is 300 cu. m and height is 15 m.

Solution:

Given,

Volume of Square Pyramid (V) = 300 m³
Height (h) = 15 m

Using the Gormula,

V = 1/3 × A × h

⇒ VA = (3V)/h

⇒ VA = 3 (300)/15

⇒ VA = 60 m²

Thus, the area of square base of the pyramid is 60 m²

Example 3: Find the height of the square pyramid if its volume is 450 m³ and the area of the square base is, 45 m².

Solution:

Given,

Volume of Square Pyramid (V) = 450 m³
Area of Square base of Square Pyramid (V) = 45 m³

Using the Formula,

V = 1/3 × A × h

⇒ h = (3V)/A

⇒ h = 3 (450)/45

⇒ h = 30 m

Thus, the height of square pyramid is 30 m.

Example 4: Find the volume of the square pyramid if the height of the square pyramid is 8 m and the side of the square base is 6 m.

Solution:

Given,

Side of Square base = a = 6 m
Height of Square pyramid = h = 8 m

Using the Formula,

V = 1/3 × a² × h

⇒ V = 1/3 × (6)² × (8)

⇒ V = 96 m³

Thus, the volume of square pyramid is 96 m³.

FAQs on Volume of a Square Pyramid

Q1: What is the Volume of a Pyramid?

Answer:

The space occupied by the pyramid in the three dimensional space is called the volume of a pyramid. The mathematical formula for the volume of a pyramid is given as

Volume of Pyramid =  1/3 × Area of Base × Height

Q2: What is the Volume of a Square Pyramid?

Answer:

The space occupied by the square pyramid in 3-D space is defined as the volume of the square pyramid. It is measured in unit³ and we use units such as m³, cm³, etc, to measure the volume of the square pyramid.

Q3: How to find the Volume of a Square Pyramid?

Answer:

The volume of a square pyramid is calculated using the formula,

Volume of Square Pyramid = 1/3 × Area of Base × Height

It is measured in cubic units.

Q4: How to Find the Height of a Square Pyramid when the Volume is Given?

Answer:

If the volume of the square pyramid and the area of the base of the square pyramid is given then its height can easily be calculated using the formula,

Height = 3 × (Volume of Square Pyramid) / Area of Base

Q5: How does the Volume of a Square Pyramid relate to the Volume of a Square Prism?

Answer:

The volume of a square pyramid and the volume of a square prism have the relation,

Volume of a Square Pyramid = (1/3) Volume of a Square Prism

This relation is valid only when the square pyramid and the square prism have the same dimensions.

Q6: What is Volume of a Square Pyramid Formula?

Answer:

The volume of the Square pyramid is calculated using the formula,

Volume of Square Pyramid = 1/3 × a²h

Where,

• a is the length of the base of a square pyramid, and 
• h is the height of a square pyramid.