Prisms are solid shapes with identical polygon ends and flat parallelogram sides.
Prisms are of different types named as triangular prisms, square prisms, rectangular prisms, pentagonal prisms, hexagonal prisms etc. A rectangular prism is of two types. They are the right rectangular prism and oblique rectangular prism. In this article, we will discuss rectangular prisms, their properties, formulas to calculate the area and volume of a prism.
Let us learn more about rectangular prism, right rectangular prism, cuboids, and cubes with the help of Rectangular Prism.
Definition of Right Rectangular Prism
A prism having a rectangular base is called a rectangular prism. A right rectangular prism is a prism that has six faces and all the faces are rectangles. All angles formed are right angles.
Rectangular prism shape consists of the following properties:
Vertices of a rectangular prism = 8
Edges of a rectangular prism = 12
Faces of a rectangular prism= 6 (including bases)
The below diagram represents a right rectangular prisms
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Rectangular Prism Examples
Examples of rectangular prism shaped objects are Rectangular tissue box, school notebooks, binders, laptops, doors, containers, cabinets, mobiles, cereal boxes, fish tanks etc.
Large structures such as cargo containers, buildings, storage sheds, and skyscrapers are also an example of a rectangular prism.
Attributes of a Rectangular Prism
A rectangular prism has 6 faces(each of the faces is rectangular).
It has 12 sides and 8 vertices.
The pairs of opposite faces of a rectangular prism are equal.
There are two types of rectangular prisms named a right rectangular prism and non-right rectangular prisms ( also known as an oblique rectangular prism).
Right Rectangular Prism Formula
Lateral Surface Area of a Rectangular Prism
The lateral surface area of a rectangular prism is the sum of the surface area of all its faces excluding the base of the rectangular prism. The lateral surface area of any right rectangular prism is calculated using the perimeter of the base times the height of the prism.
Therefore, the lateral surface =P.h square units
Where P is the perimeter of a base
h be the height of the prism
Therefore, the lateral surface area of a rectangular prism =2(l+w)h square units
Rectangular Prism Surface Area
The surface area of a rectangular prism is the measure of how much exposed area a prism covers. It is expressed in square units. The surface area of a rectangular prism is the sum of the lateral surface area along with twice the base area of the rectangular prism.
Surface area of a rectangular prism = sum of surface area of six faces =lw+lw+wh+wh+lh+lh=2(lw+wh+lh) square units
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Rectangular Prism Volume
The volume of a rectangular prism is a measurement of how much volume is occupied by a rectangular prism. The volume of a rectangular prism is denoted by cubic units. It can also be defined as the number of units used to fill a rectangular prism.
The volume of the rectangular prism is calculated by using the area of the base times its height.
Hence, the volume of a rectangular prism formula is given by the formula
The volume of a Rectangular Prism (V)= lwh cubic units
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How Does a Rectangular Prism Look Like?
Right Rectangular Prism
In a right rectangular prism:
The angles between the base and the sides are right angles.
All rectangular prism faces are rectangles.
Each corner of the prism is represented by a right angle.
All the base and top of the prism are congruent.
Right Prisms
A right prism is in the shape of a geometric solid that has a polygon as its base and vertical sides perpendicular to the base. The base and top surface are of the same shape and size. It is called a “right” prism because the angles between the base and sides are right angles. Examples of right prisms are a rectangular prism, a cube, a triangular prism and a cylinder.
Net of a Right Rectangular Prism:
The net of a 3D object is used to show the faces of that object when it is opened flat. We can form a right rectangular prism using its net as shown in the below diagram. Each face of the net is a rectangle that contains the right angles.
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Solved Examples:
1.Find the volume of a rectangular prism whose length, width, and height are 7cm, 6cm, and 4cm, respectively.
Sol: Given Length, l = 7 cm
Width, w = 6 cm
Height, h = 4 cm
The volume of a rectangular prism is, given by l.w.h
V = l x w x h cubic units
Put the value of l,w and h in the formula
V = 7 x 6 x 4 cm³
V = 168 cm³
Therefore, the volume of a rectangular prism is 168 cm³
2.Find the area of a rectangular prism whose length, width, and height are 7cm, 6cm, and 4cm, respectively.
Sol:Given:
Length, l = 7 cm
Width, w = 6 cm
Height, h = 4 cm
The formula to find the area of a rectangular prism is, 2(lh+wh+lw)
Put the value of l,w and h in the given formula
A=2(lh+wh+lw)
A=2(7x4+6x4+7x6)
A=2(28+24+42)
A=2(94)
A=188 sq.cm
3. Tim wanted to add soil to his gardening bed which resembles the shape of a rectangular prism and has the following dimensions:length = 8 ft, width = 4 ft, and height = 1 ft. Calculate the maximum amount of planting soil that can be used to fill the gardening bed?
Sol: Tim's gardening bed resembles that of a rectangular prism having the following dimensions:
Length, l = 8 ft
Width, w = 4 ft
Height, h = 1 ft
The maximum amount of planting soil that can be used to fill the gardening bed = Volume of the bed = l x w x h
After putting the value of l,w and h, 8 x 4 x 1 = 32 cubic feet.
Therefore 32 cubic feet of soil can be used.
Conclusion:
A right rectangular prism has six faces- the base, the top, and the four sides.
The base and top of the rectangular prism always have the same area, similar is the case for its pairs of opposite sides. A rectangular prism consists of 12 edges, 6 faces and 8 vertices.
Formula to Calculate Volume and Surface area is given as:
The volume of Rectangular Prism: V=lwh cubic units
Surface Area of Rectangular Prism: S =2(lw+lh+wh) square units.
FAQs on Right Rectangular Prism
1. What exactly is a right rectangular prism?
A right rectangular prism is a three-dimensional solid shape that has six faces, all of which are rectangles. The key characteristic is that its side faces are perpendicular (at a right angle) to its rectangular bases. This is why it is called a 'right' prism. In everyday language, it's often referred to as a cuboid.
2. What are the main properties of a right rectangular prism?
A right rectangular prism has a consistent set of properties as per the NCERT syllabus. These are:
It has 6 rectangular faces.
It has 12 edges.
It has 8 vertices (corners).
The angles between the bases and the side faces are all 90 degrees.
Opposite faces are parallel and identical (congruent).
3. How do you calculate the volume and surface area of a right rectangular prism?
To calculate the volume and surface area of a right rectangular prism with length (l), width (w), and height (h), you can use the following standard formulas:
Volume (V): The space the prism occupies is calculated as V = l × w × h.
Total Surface Area (TSA): The sum of the areas of all six rectangular faces is calculated as TSA = 2(lw + lh + wh).
These formulas are fundamental in the Mensuration chapter of the CBSE Maths syllabus.
4. What are some common real-world examples of a right rectangular prism?
You can find examples of right rectangular prisms all around you. Some common ones include:
A shoebox
A textbook or a notebook
A brick
An aquarium
A cereal box
These objects all have six rectangular faces and right angles between their sides and base.
5. What is the 'net' of a right rectangular prism and why is it useful?
The net of a right rectangular prism is a 2D pattern that can be folded to form the 3D shape. Imagine unfolding a cardboard box so it lies flat; that flat shape is its net. It is important because it helps in:
Visualising the shape: It shows all six rectangular faces in a single plane.
Calculating surface area: By finding the area of the 2D net, you are actually calculating the total surface area of the 3D prism.
6. Are a cuboid and a right rectangular prism the same thing?
Yes, for all practical purposes in the CBSE curriculum, a cuboid and a right rectangular prism refer to the same shape. The term 'right rectangular prism' is a more formal geometric name that precisely describes its properties: it's a prism with rectangular bases and its sides are at a right angle to the base. 'Cuboid' is the more common name for this shape.
7. How does the volume of a right rectangular prism change if its height is doubled?
If the height of a right rectangular prism is doubled while its length and width remain the same, its volume will also double. This is because the volume formula is V = length × width × height. Since the height is a direct multiplier, doubling it directly doubles the final volume. For example, if the original volume is 30 cm³, doubling the height will result in a new volume of 60 cm³.
8. What is the primary difference between a right rectangular prism and a pyramid?
The primary difference lies in their structure and number of bases. A right rectangular prism has two identical rectangular bases (a top and a bottom) connected by four side faces. In contrast, a pyramid has only one base (which can be a rectangle or another polygon) and its other faces are triangles that meet at a single point called the apex.
