How to Calculate Volume and Surface Area of a Right Rectangular Prism
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: Key Concepts and Formulas
1. What is a right rectangular prism?
A right rectangular prism is a three-dimensional shape with six rectangular faces, where each angle between the faces is a right angle. It is commonly called a rectangular box. All faces are rectangles, and opposite faces are equal in size.
2. What are the key properties of a right rectangular prism?
A right rectangular prism has the following key properties:
- Six rectangular faces
- Twelve edges
- Eight vertices
- All angles are right angles
- Opposite faces are equal in area
3. How do you find the volume of a right rectangular prism?
To find the volume of a right rectangular prism, multiply the length, width, and height together. The formula is $\text{Volume} = \text{length} \times \text{width} \times \text{height}$. This calculates the space the prism takes up inside.
4. What is the formula for the surface area of a right rectangular prism?
The surface area of a right rectangular prism is found with the formula $2(lw + lh + wh)$, where $l$ is length, $w$ is width, and $h$ is height. This formula adds the areas of all six faces of the prism.
5. What is the difference between a rectangular prism and a cube?
A cube is a special case of a rectangular prism where all sides are equal in length. In contrast, a right rectangular prism has three sets of opposite faces that can be different sizes.
6. Where are right rectangular prisms used in real life?
Right rectangular prisms are seen in daily life in items like
- cardboard boxes
- bricks
- books
- building blocks
7. How do you identify a right rectangular prism from other 3D shapes?
A right rectangular prism can be identified by checking:
- It has six rectangular faces
- All faces meet at right angles
- Opposite faces are equal
8. Are all boxes right rectangular prisms?
Not all boxes are right rectangular prisms. Only those with all faces as rectangles and every angle a right angle qualify. Boxes with slanted sides or non-rectangular faces do not fit the definition of a right rectangular prism.
9. Can a right rectangular prism have square faces?
Yes, a right rectangular prism can have square faces if two or more sides are equal in length. When all sides are equal, every face becomes a square, and the prism is then called a cube, which is a special type of rectangular prism.
10. What units are used for calculating volume and surface area of a right rectangular prism?
For a right rectangular prism,
- volume is measured in cubic units (such as cm³, m³)
- surface area is measured in square units (such as cm², m²)
11. What is the difference between a prism and a right prism?
A right prism is a prism whose sides are perpendicular to its base. In a general prism, the sides may be slanted or oblique, but in a right prism, all sides meet the base at a right angle.
12. How is the diagonal of a right rectangular prism calculated?
The diagonal of a right rectangular prism is found using the formula $\sqrt{l^2 + w^2 + h^2}$, where $l$ is length, $w$ is width, and $h$ is height. This formula applies the Pythagorean theorem in three dimensions.
