How To Get The Volume Of A Rectangular Prism

Volume of Rectangular Prism

The volume of a rectangular prism is the measurement of the total capacity it can hold. Imagine having a rectangular container filled with water. In this case, the total quantity of water that the container can hold is its volume. A prism is a polyhedron, a solid three-dimensional object having identical bases, flat rectangular side faces, and the same cross-section all along its length. Prisms are classified as per the shape of their base. A rectangular prism is categorized as a three-dimensional shape. It has six faces and all the faces of the prism are rectangles. There is a formula to find the volume of a rectangular prism which we are going to learn on this page.

1.	What is the Volume of Rectangular Prism?
2.	Volume of Rectangular Prism Formula
3.	How To Calculate Volume of Rectangular Prism?
4.	FAQs on Rectangular Prism

What is the Volume of Rectangular Prism?

The volume of a rectangular prism is defined as the space occupied within a rectangular prism . A rectangular prism is a polyhedron that has two pairs of congruent parallel bases. By definition, it is because of its cross-section along the length, that it is considered to be a prism . It has 6 faces(all are rectangular),12 sides, and 8 vertices, two pairs of opposite faces that are equal, a rectangular cross-section, and the same cross-section along the length. As the rectangular prism is a three-dimensional shape, thus, the volume of the rectangular prism lies in the three-dimensional plane as well.

Volume of Rectangular Prism Formula

To recall, a rectangular prism is characterized by its 2 parallel rectangular bases and 4 rectangular faces. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid. The volume of any prism is the capacity that it can hold or the space occupied by it and we know that the volume of any prism is obtained by multiplying its base area by its height. i.e., the volume of a prism = base area × height. Thus, the volume of a rectangular prism formula can be obtained by multiplying the length, breadth, and height of the prism and is measured in cubic units (cm³, m³, in³, etc). We will discuss the formulas to calculate the volumes of different types of rectangular prisms.

We will use this formula to calculate the volume of a rectangular prism as well. We know that the base of a rectangular prism is a rectangle. By applying the above formula to a rectangular prism, we get, volume of a rectangular prism (V) = l × w × h, where

"w" is the base width
"l" is the base length
"h" is the height

Volume of Rectangular Prism
The volume of a rectangular prism = area of base × height

To find the volume of the rectangular prism, we multiply the length, breadth, and height, that is the area of the base multiplied by the height. Thus, we give the volume of any rectangular prism by taking length times width times height. Now that the third dimension of measurements has come into the picture, thus the unit will be cubic units like these cubic centimeters.

There are two types of rectangular prisms, namely right rectangular prisms and non-right rectangular prisms or oblique prisms.

Rectangular Prism Formula for the Right Rectangular and Oblique Prism

In the case of a right rectangular prism, the bases are perpendicular to each other.
In the case of an oblique rectangular prism, the bases are not perpendicular to each other. Thus, the perpendicular drawn from one vertex of one base to the other base of the prism will be taken as its height.

Note that you can apply the same formula, that is the rectangular prism volume formula, v = lwh, irrespective of the type of rectangular prism.

How To Calculate Volume of Rectangular Prism?

Before calculating volume using the formula, make sure that all measurements are of the same units. Here are the steps to calculate the volume of a rectangular prism.

Step 1: Identify the type of the base and find its area using a suitable formula (as explained in the previous section).
Step 2: Identify the height of the prism, which is perpendicular from the top vertex to the base of the prism.
Step 3: Multiply the base area and the height.
Step 4: Write the answer with an appropriate unit.

Example: Calculate the volume of the rectangular prism whose height is 8 in and whose base area is 90 square inches.

Solution:We can calculate the volume of the rectangular prism using the following steps:

Step 1: The base area is already given as 90 square inches.
Step 2: The height of the prism is 8 in.
Step 3: The volume of the given rectangular prism = base area × height = 90 × 8 = 720 cubic inches.

Example 1: Determine the height of a rectangular prism that has a base area of 10 sq. units and a volume of 40 cubic units.

Solution: Given the volume of the rectangular prism = 40 cubic units and the base area of the rectangular prism= l x b = 10 sq units.

Using the volume of the rectangular prism formula, base area × height = 40 cubic units.
The height of the given rectangular prism = 10 × height = 40.

Thus, the height of the rectangular prism = 40/10 = 4 units
Example 2: Given the base length, base width, and height of the rectangular prism as 8 in, 5 in, and 16 in respectively. Find the volume of the rectangular prism?

Solution: Given that: The base length of the rectangular prism is, l = 8 in, and its breadth is b = 5 in.

So the base area = l × b = 8 × 5 = 40 sq inches.
The height of the prism is h = 16 in.

Using the volume of the rectangular prism formula, the volume of the given rectangular prism = base area × height = (40 × 16) = 640 cubic inches.

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FAQs on Volume of Rectangular Prism

What is the Volume of a Rectangular Prism?

The volume of a rectangular prism is the space inside it. Thus, the volume of a rectangular prism can be calculated by multiplying its base area by its height. The volume of a rectangular prism can be expressed in cubic units such as cm³, m³, in³, etc.

What is the Formula for Finding the Volume of a Rectangular Prism?

The volume of a rectangular prism follows the simple method, multiply all three dimensions - length, height, and width. Thus, the volume of the rectangular prism is given by the formula V= l × w × h where"V", "l" "w", and "h" are the volume, length, width, and height of the rectangular prism respectively.

How to Find the Volume of a Rectangular Prism?

To find the volume of a rectangular prism, follow the steps given below:

Step 1: Identify the length and width of the base of the prism
Step 2: Find the height(total height) of the prism.
Step 3: Put the respective values in the formula, V = lwh
Step 4: Multiply the length of the prism by the width of the prism by the height of the prism.
Step 5: Write the product so obtained with the appropriate unit.

How do you Find the Height of a Rectangular Prism when the Volume of a Rectangular Prism is given?

The volume of a rectangular prism with the given dimensions is the area of the base times the height. Thus, to calculate the height, divide the volume of a prism by its base area. Suppose that the volume of the prism is 600 cubic units and its base area is 60 square units. Then, dividing 600 by 60 results in 10. Therefore, the height is 10 units.

What Happens to the Volume of Rectangular Prism If Its Height is Doubled?

We know that the volume of a rectangular prism is lwh, which is the product of its three dimensions. If its height will be doubled, its volume v' will be lw(2h) = 2lwh = 2v. Thus, we can say that the volume of the rectangular prism also gets doubled when its height is doubled.

What Happens to the Volume of Rectangular Prism If the Length is Doubled and the Height is Reduced to One Half?

The formula for calculating the volume of a rectangular prism is lwh, If its length will be doubled, and height will be reduced to half, then its volume v' will be (2l)(w)(1/2h) = 2/2lwh = v. Thus, we can say that the volume of the rectangular prism will remain same if its length gets doubled and height reduced to half.

What Happens to the Volume of Rectangular Prism If the Length, Width, and Height of Prism are Doubled?

The volume of a rectangular prism is the product of its three dimensions, that is lwh, if its length, width, and height will be doubled, then its volume v' will be (2l)(2w)(2h) = 8lwh = 8v. Thus, we can conclude that if its length, width, and height will be doubled, the volume of the rectangular prism will be 8 times the original value.