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.

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 1 What Is the Volume of Square Prism? 2 How To Calculate the Volume of Square Prism? 3 FAQs on Volume of Square Prism

What Is the Volume of 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 = hOn substituting the values in (1)The volume of square prism formula: a2 hWhere,

a = side of a square prismh = height of the square prism

How To Calculate the Volume of 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 = 10V = 72 × 10V = 490 inch3Therefore, the volume of square prism is 490 inch3.

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Example 2: The volume of a square prism is 784 inches3 and the height of a square prism is 16 inches respectively. Find the edge of the square prism.

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Solution:Given parameters, the height of prism (h) = 16 inches and volume of a square prism is 784 inches3Volume of square prism = a2h cubic units = (a2) × (h).Where "a" is an edge of the square prism base and "h" is the height of the prism.On substituting the values in the formula784 = (a2) × (16)a2 = 784 ÷ 16a2 = 49a = √49a = 7 inches.