[Maths Class Notes] on Volume of a Rectangular Prism Formula Pdf for Exam

A three-dimensional solid structure with six rectangular sides is known as a rectangular prism. The rectangular prism is also known as a cuboid prism. It contains eight vertices, twelve edges, and six faces. The rectangular prism is best represented by bricks, boxes, and books. The form of a rectangular prism is seen in the diagram below.

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Edge: An edge is a line segment that connects with two vertices. In a rectangular prism, there are a total of twelve edges. The lengths of these edges vary.

Face: The rectangular sides of a rectangular prism are called faces. In a rectangular prism, there are six faces (top, bottom, right, left, front, and rear). The opposing faces are similar.

Vertex: The vertex is the place where three edges or the corners of the form meet. In a rectangular prism, there are eight vertices in total.

Types of Rectangular Prism

There are 2 Types of a Rectangular Prism

1. Right Rectangular Prism: A rectangular prism has all of its angles to be right angles. In other terms, the right rectangular prism is a rectangular prism with bases that are perpendicular to each other. The form of a right rectangular prism is seen in the diagram below.

2. An oblique rectangular prism is one in which all of the angles are not right angles. In other terms, an oblique rectangular prism is a rectangular prism with bases that are not perpendicular to each other. The form of an oblique rectangular prism is seen in the diagram below.

Properties of Rectangular Prism

• A rectangular prism forms a rectangular cross-section.

• A rectangular prism has 6 rectangular faces, 12 edges, and 8 vertices.

• All the opposite faces are in rectangle shape.

• It is also known as a cuboid.

Volume of Rectangle Formula

The amount of space occupied by a three-dimensional object is called the volume of that object. The volume of a rectangular prism represents the amount of space it occupies. In other words, the volume of a rectangular prism is defined as the number of units utilised to fill it. A cubic unit is a unit of volume.

Volume of Rectangle Formula in Maths

The volume of rectangle formula in maths is given by:

Volume of Rectangle formula (V)= l × w × h.

Here,

l  signifies length of the rectangular prism

B signifies the base of a rectangular prism

w is the width of a rectangular prism

Volume of a Rectangular Prism Formula

The volume of the rectangle formula is the product of length (l), width (w), and height (h). It is denoted by V.

Therefore, the volume of rectangular prism formula can be written as:

Volume of a Rectangular Prism formula (V)= length × width × height

Or

Volume of Rectangle formula (V)= l × w × h

Where,

l is the length of a rectangular prism

B is the base of a rectangular prism

W signifies the width of a rectangular prism

Area of a Rectangular Prism Formula

Rectangular prism area formula  (S) =  2(lw + lh + wh)

Solved Examples

Let’s Solve Some Examples Based on the Above Formulas.

Ex.1. The length, width, and height of a rectangular prism are 16 cm, 12 cm, and 8 cm, respectively. Find the volume of a rectangular prism?

Solution:

Given, length = 16 cm,

width = 12 cm,

height = 8 cm.

By the volume of prism formula, we have

Volume = l*w*h

= (16*12*8) cm³

= 1536 cm³

Hence the volume of a rectangular prism is 1536 cm³

Ex.2.  The length, width, and height of a rectangular prism are 24 cm, 21 cm, and 12 cm, respectively. Find the volume of a rectangular prism?

Solution:

Given, length = 24 cm,

width = 21 cm,

height = 12 cm.

By the volume of rectangular box formula, we have

Volume = l*w*h

= (24*21*12) cm³

= 6048 cm³

Hence the volume of a rectangular prism is 6048 cm³

Ex.3. The length, width, and height of a rectangular prism are 4 cm, 5 cm, and 2 cm, respectively. Find the volume of a rectangular prism and also find the surface area of a rectangular prism.

Solution

Given, length = 4 cm,

width = 5 cm,

height = 2 cm.

By the volume of a rectangular prism formula, we have

Volume = l*w*h

= (4*5*2) cm³

= 40 cm³

Hence the volume of a rectangular prism is 40 cm³

Using the surface area of a rectangular prism formula, we have

Rectangular prism area formula  (S) =  2(lw + lh + wh)

Rectangular prism area formula  (S) =  2(45 + 42 + 52)

Rectangular prism area formula  (S) = 76 m²

Hence the  surface area of a rectangular prism is 76 m²