What is a Right Rectangular Prism? Definition With Examples

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What Is a Right Rectangular Prism?

In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has 6 faces with its base as rectangles. Rectangular prisms can be of two types, namely right rectangular prisms and non-right (oblique) rectangular prisms.

Right and non-right rectangular prisms

The right rectangular prism has two parallel end faces and four lateral faces, each one of which is a rectangle; the faces are perpendicular to each of its bases. The faces of a non-right rectangular prism (oblique prism) are parallelograms. 

A right rectangular prism is also called a cuboid.

A solid cuboid

We can find the shape of a right rectangular prism all around us—in a truck, a chest of drawers, and an aquarium. 

Real life examples of right rectangular prisms


Properties of a Right Rectangular Prism:

  • It has 8 vertices, 12 sides, and 6 rectangular faces.
  • All its opposite faces are congruent. 
  • The angle between its base and sides is 90 degrees or right angle.
  • All its faces are rectangles and parallel.

Surface Area and Volume of a Right Rectangular Prism

Let’s consider this right rectangular prism with the marked length, width, and height. 

A cuboid with marked length, width, and height

Since all its faces are rectangles and opposite faces are equal, the surface area of a right rectangular prism can be calculated using the following formula:

Lateral Surface Area = 2 × height (length + width)


Total Surface Area = 2 {( width × length )+( length × height ) + (width × height )}

Volume of a right rectangular prism is obtained by multiplying all three dimensions—length, height, and width—or by multiplying the base area with its height.

Volume = length ×  width × height

OR

Volume = Area of base × height

Fun Facts

Rectangular prisms are the most commonly used prisms in real life, especially in packaging—from cereal boxes to cartons and parcels delivered by mail.  

Solved Examples

Example 1: Find the volume of the given cuboid.

A cuboid with length, width, and height marked as 15 cm, 3 cm, and 7cm

Solution:

length = 15 cm; width = 3 cm; height = 7 cm

Volume = length × width × height

= 15 × 3 × 7 cm3

= 315 cm3

Example 2: Find the volume of the rectangular prism with a base area of 105 square meters and a height of 4 meters.

Solution: 

Volume = Area of base × height

= 105 × 4 m3

= 420 m3

Example 3: A foam company manufactures mattresses. Their king-sized mattress is approximately 183 cm by 183 cm, with a thickness of 12.5 cm. Find the total surface area of the mattress.

 Solution: 

length = 183 cm

width = 183 cm

height = 12.5 cm

Total surface area = 2 {(width × length) + (length × height) + (width × height)}

= 2 {(183 × 183) + (183 × 12.5) + (183 × 12.5)} cm2

= 2 {33,489 + 2,287.5 + 2,287.5} cm2

= 2 {38,064} cm2

= 76,128 cm2

Example 4: Find the area of an iron sheet required to construct a closed container of length 5 m, height 6.5 m and width 2.3 m.

Solution: 

To find the iron sheet required, we need to find the total surface area of a cuboid with the given dimension.

Total surface area = 2 {(width × length) + (length × height) + (width × height)}

= 2 {(2.3 × 5) + (5 × 6.5) + (2.3 × 6.5)} m2

= 2 {(11.5) + (32.5) + (14.95)} m2

= 2 {58.95} m2

= 117.9 m2So, a 117.9 m2 iron sheet is required to construct the container.

Practice Problems

Lateral surface area = 2 { (L $\times$ H) + (W $\times$ H)}

Lateral surface area = 2 { (4 $\times$ 9) + (4 $\times$ 9)}

= 2 ( 36 + 36 ) = 144 ft2

Practice Problems

What is a Right Rectangular Prism? Meaning, Definition, Examples

Attend this Quiz & Test your knowledge.

1

A right rectangular prism has ______ edges.

6
8
12
20
CorrectIncorrect
Correct answer is: 12
A right rectangular prism has 12 edges.
2

What is the horizontal cross-section of a right rectangular prism?

Circle
Parallelogram
Triangle
Rectangle
CorrectIncorrect
Correct answer is: Rectangle
A horizontal cross section of a right rectangular prism is a rectangle in shape.
3

How many small cuboidal boxes, with length 5 cm, width 4 cm, and height 2 cm, can be kept in the cuboidal container of length 35 cm, width 24 cm and height 18 cm?

378
1,512
756
1,890
CorrectIncorrect
Correct answer is: 378
Number of small cuboidal boxes = $\frac{35 × 24 × 18}{5 × 4 × 2}$ = 378
4

Which box will need the least amount of paint? The length, width, and height of boxes are

Box 1: 7 cm, 14 cm, 9 cm
Box 2: 5 cm, 18 cm, 10 cm
Box 3: 8 cm, 7 cm, 15 cm
Box 4: 4 cm, 9 cm, 20 cm
CorrectIncorrect
Correct answer is: Box 1: 7 cm, 14 cm, 9 cm
The box that has the least total surface area needs the least amount of paint. So, we need to find the total surface area of each box. Box 1: 574 cm2; Box 2: 640 cm2; Box 3: 562 cm2; Box 4: 592 cm2.

Frequently Asked Questions

The right rectangular prism has 6 faces, 8 vertices (corners), and 12 edges, and its faces are perpendicular to each of its bases.

Yes, the formula for volume is the same. Volume = length of base × width of base × height.

The right rectangular prism has two parallel end faces and four lateral faces, each one of which is a rectangle; the faces are perpendicular to each of its bases. The faces of a non-right rectangular prism (oblique prism) are parallelograms.

The right rectangular prism is commonly called a cuboid.

No, cube and cuboid are not the same. For cubes, all its faces are square while cuboid faces are rectangles in shape.