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Combine Volumes of Prisms

Key Concepts

  • Composite figures
  • The volume of the composite figure

11.3 Combine volumes of Prisms 

The shape and size of a kitchen storage are shown in the figure. Ria’s mother wants to find the volume to determine how much storage space is available. What is the volume? 

11.3.1 Composite figures 

A composite or compound shape is any shape that is made up of two or more geometric shapes. 

The image below is an example of composite figures. 

Two rectangular prisms formed into one rectangular prism. 

Example1:  

This image below can be separated into two rectangular prisms, as shown. 

Identify the measurement for the length, width and height of each prism. 

Solution: 

Step 1: The length, width and height of prism A.  

Length = 4 m 

Width =9 m 

Height =5 m 

Step 2: The length, width and height of prism B. 

Length = 10 m 

Width =9 m 

Height =7 m 

Example 2: 

Identify the measurement for the length, width and height of each prism. 

Solution: 

Step1: The length, width and height of the small prism.  

Length = 8 m  

Width =4 m 

Height =2.5 m  

Step 2: The length, width and height of the big prism. 

Length = 12 m 

Width =4 m 

Height =15 m 

11.3.2 Volume of the composite figures             

Example 1: Find the volume of composite figures. 

Solution: 

Step1: Use the formula V= l x w x h to find the volume of each rectangular prism. 

Step2: Volume of prism A 

   = 6 × 4 × 3  

   = 72  

Step 3:       

= 8 × 4 × 7 

=>32 × 7 = 224 

Step 4: Add to find the total volume. 

72 + 224 = 296 

The volume of the composite figure is 296 cubic meters. 

Example 2: 

Find the volume of the composite figure. 

Solution: 

Step1: Use the formula to find the volume of each rectangular prism. 

Step2: Volume of prism A 

= 10 × 30 × 30  

= 9,000  

Step3: Volume of prism B  

 = 20 × 30 × 20 

= 12,000 

Step 4: Add to find the total volume. 

9,000 + 12,000 = 21,000  

The volume of the composite figure is 21,000 cubic centimetres.

   

Example 3: 

What is the volume of the composite figure? 

Solution:  

Step 1: To find the volume of the figure, start by breaking it up into 2 rectangular prisms. 

Step 2: Now, find the volume of each prism. Start with the back prism. 

The length ℓ is 10 meters. The width w is 5 meters. The height h is 8 meters. 

V = 10 × 5 × 8 

V = 400 

The volume of the back prism is 400 cubic meters. 

Step 3: Then, find the volume of the front prism. 

The length ℓ is 6 meters. The width w is 2 meters. The height h is  

4 meters. 

V = 6 × 2 × 4 

V = 48  

The volume of the front prism is 48 cubic meters. 

Step 4: To find the total volume of the figure, add the volumes of the prisms. 

Step 5: 400+48=448 

The volume of the figure is 448 cubic meters. 

Exercise:

  1. Find the length, width and height of rectangular prism 1.

2. Find the volume of rectangular prism 2.

3. Find the volume of the given rectangular prism.

4. Find the volume of the given figure.

5. Find the volume of the rectangular prism.

6. Find the volume of the bottom rectangular prism.

7. Find the volume of the rectangular prism.

Concept Map

What Have We Learned:

  • Understanding how to combine the volume of prisms.
  • Understanding cube and rectangular prism.
  • How to find the volume of composite figures

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