Volume of Square Prism

The volume of square prism is nothing but the total amount of vacuum or space that is occupied by the prism which has a square as its base. A square prism is a three-dimensional cuboid. In the square prism, the base and top are congruent squares. The remaining 4 faces of the square prism are rectangles. In this article, we will cover the method behind calculating the volume of a square prism.

The volume of a square prism is referred to as the amount of space occupied by a 3-dimensional prism that has two congruent square bases and four rectangular faces are known as the volume of square prism. It is measured in cubic units. The volume of a prism is the product of the cross-sectional area and its length. The cross-sectional area is also known as the base area of the square prism.

Volume of Square Prism Formula

Let us consider a square prism with a square base.
V = Area of base × Height of the prism...(1)
Area of base = a × a = a² (Since the bases are squares and the area of the square is edge²)
Height of prism = h
On substituting the values in (1)
The volume of square prism formula: a² h
Where,

• a = side of a square prism
• a² = base area of square
• h = height of the square prism

The steps to determine the volume of a square prism are:

• Step 1: Note down the given dimensions of the square prism. Such that a = side of a square prism, a² = base area, h = height of the square prism. Note that the units of a and h should be the same.
• Step 2: Substitute the respective dimensions in the volume of square prism formula a² h.
• Step 3: The value of the volume of the square prism is obtained and write the unit of the volume of the square prism in terms of units³.

Let us consider the following example:

Example: If the length of the side of the square face of a square prism is 7 inches and its height is 10 inches, find the volume of square prism.

Solution:

Given: side of the square prism, a = 7 inches; height of the square prism, h = 10 inches; Using the volume of square prism formula:
The volume of a square prism, V = a²h. Substituting the values of a = 7, h = 10
V = 7² × 10
V = 490 inch³
Therefore, the volume of square prism is 490 inch³.

Related Topics

Listed below are a few interesting topics related to volume of square prism, take a look.

• Square Prism Formula
• Volume of Prism
• Volume of a Square Pyramid

What Is the Volume of Square Prism?

The amount of vacuum occupied by a square prism is referred to as the volume of square prism. The volume of square prism depends on the edge of the square base and the height of the prism. The volume of square prism is given as a² h (where, a = side of a square prism, a² = base area, h = height of the square prism). The unit of volume of square prism is expressed in m³, cm³, in^3, and so on.

What Is the Formula for Volume of Square Prism?

The formula for the volume of square prism is (base area) × (height of the square prism). To find the volume of the square prism we use the general formula: a² h. Here "a" is an edge of the base of the square prism and "h" is the height of the square prism.

How To Find the Volume of Square Prism?

We can find the volume of square prism using the following steps:

• Step 1: Observe the pattern of the square prism. Write down the given dimensions of the square prism such as the dimension of the edge (a), the height of the square prism (h).
• Step 2: Substitute the dimensions in the general volume of square prism formula: V = a² h
• Step 3: The value of the volume of square prism is obtained and write the unit of the volume as units³.

How Do You Find the Height of Square Prism if the Volume of Square Prism and Edge of Base Are Given?

The steps to determine the height of the square prism, if the volume of square prism and edge of base is given, is:

• Step 1: Write the given dimensions of the prism, volume (V), and edge (a).
• Step 2: Substitute the given values in the formula V = a² h.
• Step 3: Now solve the equation for the height (h) of the square prism.

What Happens To the Volume of Square Prism If the Height of Square Prism Is Doubled?

The volume of the square prism depends on the edge of the prism and the height of the square prism. The volume of a square prism is given as V = a² h, hence V is directly proportional to h. Thus, the final value of the volume of the square prism will get doubled if the height of the square prism is doubled.

How Do You Find the Edge of Square Prism if the Volume of Square Prism and Height of Prism Are Given?

The steps to determine the edge of the square prism, if the volume of square prism and height is given, is:

• Step 1: Write the given dimensions of the prism. Volume (V) and height (h).
• Step 2: Substitute the given values in the formula, V = a² h (where, a = side of a square prism)
• Step 3: Now solve the equation for the edge (a) of the square prism.