Right Rectangular Prism formula for volume and surface area with examples
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 Explained with Properties and Formulas
1. What is a right rectangular prism?
A right rectangular prism is a three-dimensional solid with six rectangular faces and all angles equal to 90°. It has:
- 6 rectangular faces
- 12 edges
- 8 vertices
2. What is the formula for the volume of a right rectangular prism?
The volume of a right rectangular prism is given by V = l × w × h. Here:
- l = length
- w = width
- h = height
3. How do you find the surface area of a right rectangular prism?
The surface area of a right rectangular prism is calculated using SA = 2(lw + lh + wh). To find it:
- Find the area of each pair of opposite faces: lw, lh, and wh
- Add them together
- Multiply the sum by 2
4. How many faces, edges, and vertices does a right rectangular prism have?
A right rectangular prism has 6 faces, 12 edges, and 8 vertices. Specifically:
- 6 rectangular faces
- 12 straight edges where faces meet
- 8 corner points (vertices)
5. What is the difference between a cube and a right rectangular prism?
The main difference is that a cube has all sides equal, while a right rectangular prism does not require equal side lengths. In detail:
- Cube: l = w = h
- Right rectangular prism: l, w, and h can be different
6. How do you find the diagonal of a right rectangular prism?
The space diagonal of a right rectangular prism is found using d = √(l² + w² + h²). Steps:
- Square the length, width, and height
- Add the three squares
- Take the square root of the sum
7. What are the properties of a right rectangular prism?
The key properties of a right rectangular prism include rectangular faces and right angles. Its main properties are:
- All angles are 90°
- Opposite faces are equal and parallel
- Opposite edges are equal in length
- It has 6 faces, 12 edges, and 8 vertices
8. How do you calculate the base area of a right rectangular prism?
The base area of a right rectangular prism is calculated using Base Area = l × w. The base is a rectangle, so multiply its length and width. For example, if l = 7 cm and w = 5 cm, the base area is 7 × 5 = 35 cm². This value is also used when calculating volume.
9. What is a real-life example of a right rectangular prism?
Common real-life examples of a right rectangular prism include a box, brick, book, or room. These objects have:
- Rectangular faces
- Right angles at every corner
- Three measurable dimensions: length, width, and height
10. Why is it called a “right” rectangular prism?
It is called a “right” rectangular prism because all its angles are right angles (90°). The term “right” in geometry means the lateral edges are perpendicular to the base. This distinguishes it from oblique prisms, where the sides lean and angles are not 90°.
