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.
[Image will be Uploaded Soon]
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
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.
[Image will be Uploaded Soon]
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.
[Image will be Uploaded Soon]
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.
[Image will be Uploaded Soon]
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 on Volume of a Rectangular Prism Formula
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.
