Volume of a Rectangular Prism Formula

Rectangular Prism Definition

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.

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  1. 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.

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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.

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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

FAQs (Frequently Asked Questions)

Q1. What is the Volume of Rectangular Solid Formula?

Answer: 

The volume of rectangular solid formula is,

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

Where,

l: length of a rectangular prism

b: base of a rectangular prism

w: width of a rectangular prism

Q2.  What is the Volume of Prism Formula?

Answer: The volume of prism formula is, V = Bh where B is the base area and h is the height. The prism's base is a rectangle. The rectangle's length is 9 cm and its width is 7 cm.