Table of Contents
- What is meant by Volume?
- What is a Rectangular Prism?
- Real-world Examples of Rectangular Prisms
- Meaning of a Right Rectangular Prism
- Real-world Examples of Right Rectangular Prisms
- Properties of a Right Rectangular Prism
- The Volume of a Right Rectangular Prism
- Solved Examples
- Frequently Asked Questions
What is Meant by Volume?
In mathematics, volume can be defined as the amount of space occupied by three-dimensional solid figures. These solid figures can be cubes, cuboids, cones, cylinders, or globes.
Different shapes have different volumes. We have previously touched upon various shapes and solid objects, such as cubes, cuboids, cylinders, cones, etc. It is possible to find the volume of all these solid figures. Let’s learn more about the volume of a right rectangular prism, also known as a cuboid.
What is a Rectangular Prism?
A rectangular prism is a three-dimensional shape with two top faces, two bottom faces, and four sides. The prism’s faces are all rectangular. As a result, there are three pairs of identical faces in the picture below. A rectangular prism is also known as a cuboid because of its shape. A rectangular prism can be found in a geometry box, notebooks, diaries, rooms, and other places. The shape of a rectangular prism can be seen in the diagram below.
Real World Examples of Rectangular Prisms
A rectangular prism can be found in a truck, a chest of drawers, and an aquarium, among other places.
Meaning of a Right Rectangular Prism
A right rectangular prism is a three-dimensional shape with six faces (all of which are rectangular), twelve edges, and eight vertices. The prism’s faces are all rectangles. All of the angles formed at the vertices are right angles, or 90 degrees.
Real World Examples of Right Rectangular Prisms
Right rectangular prisms, also known as cuboids, can be found all around us. A few examples include books, boxes, buildings, bricks, boards, doors, containers, cabinets, mobile phones, and laptops.
Properties of a Right Rectangular Prism
Identifying a right rectangular prism becomes easier if we understand its basic properties that are listed below:
- Right angles exist between the base and the sides.
- All its faces are rectangular.
- A right angle is represented by each corner of the prism.
- The prism’s base and top are identical.
The Volume of a Right Rectangular Prism
The space occupied by a closed surface of a solid shape is known as the volume.
The product of the area of one face of a right rectangular prism multiplied by its height is its volume
Volume = \( l\times w\times h \) cubic units.
Where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the right rectangular prism.
Solved Volume of Rectangular Prism Examples
Example 1:
Tim wants to add some soil to his rectangular prism-shaped gardening bed, which has the following dimensions: length = 8 units, width = 4 units, and height = 1 unit. Is there a limit to how much planting soil can be used to fill the gardening bed?
Solution:
The volume of the gardening bed, which is equal to \(= l\times w\times h \) cubic units, determines the maximum amount of planting soil that can be used to fill it.
In other words,
\( 8\times 4\times 1=32 \) cubic units.
As a result, the gardening bed can be filled with 32 cubic units of soil.
Example 2:
Kevin wants to know how tall a rectangular prism with a base area of 10 square units and a volume of 40 cubic units is.
Solution:
A rectangular prism has a volume of 40 cubic units. \( (l\times w=10) \) square units, which indicates the base area. Find the height of the prism.
The volume of the rectangular prism = 40 cubic units
As a result, \( l\times w\times h=40 \)
\( (l\times w)\times h=40 \)
\( 10\times h=40 \)
\( h= \frac{40}{10} \)
\( h= 4\) units
Therefore, the prism’s height is 4 units.
A right rectangular prism is a three-dimensional object with six faces, twelve edges, and eight vertices. It is also known as a cuboid is another name for it.
The volume of a right rectangular prism is calculated by applying this formula:
Volume of a right rectangular prism = (length × width × height) cubic units.
Some real-world examples of a right rectangular prism include books, bricks, aquariums, and laptops.
Each face of a right rectangular prism resembles a rectangle.