What is Meant by Volume?
In mathematics, volume is defined as the three-dimensional space enclosed by a boundary or occupied by an object.
The blocks and books take up a lot of space here.
What is a Rectangular Prism?
A rectangular prism is a three-dimensional hexagon (two tops, two bottoms, and four sides). All of the prism’s faces are 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. It 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.
Formula for Finding the Volume of a Rectangular Prism
The occupied units of a rectangular prism are measured by the volume of the prism, which is represented in cubic units. The number of units used to fill a rectangular prism is also defined.
The area of the base multiplied by the height equals the volume of the rectangular prism.
A rectangular prism’s volume is equal to the multiplication of its length, width, and height in cubic units.
= l x w x h cubic units of volume
Where l is the length, w is the width, and h is the height of the rectangular prism.
Formula for Calculating the Volume of a Cuboid
The volume of a cuboid is the product of its dimensions, i.e., length, width, and height. The volume of a cuboid is equal to the product of its base area and height. Hence, we can write:
The volume of a cuboid = Base area × Height [Cubic units]
The base of the cuboid is a rectangle. So, the base area of a cuboid is equal to the product of its length and breadth. Hence,
The volume of a cuboid = length × breadth × height [cubic units]
or
The volume of a cuboid = l × b × h [cubic units]
where l = length , b = breadth, and h = height
Composite Figures
Two or more solid figures are combined to create a composite figure. You can determine the volume of a composite figure by dismantling it.
How Do You Calculate the Volume of Composite Shapes?
Composite shapes have a volume that is made up of basic shapes. We can calculate the volume of the composite shapes using the steps listed below:
Step 1: Break down the compound shape into different components.
Step 2: Determine the volume of each basic shape.
Step 3: Combine the volumes of all the basic shapes.
Step 4: Write the solution in cubic units.
Solved Composite Figures Examples
Question 1:
Find the volume of the composite figure.
Solution:
Make rectangular prisms out of the figure. Determine the volumes of each prism.
The volume of prism A = length × width × height
= 4 × 4 × 8
= 128 cubic feet
The volume of prism B = length × width × height
= 6 × 4 × 3
= 72 cubic feet
Total volume = volume of prism A + volume of prism B
= 128 cubic feet + 72 cubic feet
= 200 cubic feet
Hence, the volume of the composite figure is 200 cubic feet.
Question 2:
This swimming pool is 5 feet deep. How much water can the pool hold in cubic feet?
Solution:
Make rectangular prisms out of the figure. Determine the volumes of each prism.
The volume of prism A = length × width × height
= 12 × 5 × 20
= 1200 cubic feet.
Volume of prism B = length × width × height
= 40 × 5 × 10
= 2000 cubic feet.
Volume of prism C = length × width × height
= 12 × 5 × 20
= 1200 cubic feet.
Total volume = volume of prism A + volume of prism B + volume of prism C
= 1200 cubic feet + 2000 cubic feet + 1200 cubic feet
= 4400 cubic feet
Hence, the volume of the composite figure is 4400 cubic feet.
There is no particular formula for calculating the volume of composite shapes. The volume of a composite shape can be calculated by dividing it into basic shapes such as rectangles, polygons, etc. and adding up their volumes.
Adding the volumes of all the figures together yields the volume of composite shapes. The volume of composite shapes is measured in cubic units such as cubic meters, cubic feet, and so on.
The volume of any composite shape is defined as the volume that it covers. A composite shape is created by combining basic shapes. As a result, the volume of the composite shape is calculated by adding all of the basic shapes individually.