Key Concepts
- Word problems using volume
Solve word problems using volume
What is volume?
Space occupied by a 3D shape is known as its volume.
Let us consider the volume of a shape by multiplying length × width × height.
A pet shop has a large rectangular bird cage. They need 14 feets for each cage. Find the volume of space required to place all the birds inside the cage.
![What is volume?](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/f54053a3-02b4-48b6-b864-aa427a48da29.png)
![What is volume?](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7333.png)
Word problems involving volume
Jerimia built a house out of building blocks. Find the volume of the house Jerimia built.
![Word problems involving volume](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7334.png)
Solution:
Step 1: Find the volume of each section.
V = l x w x h
Step 2: Find the volume of block on the house.
V = 5 x 3 x 10
V= 150
Step 3: Find the volume of house.
V = 20 × 24 × 20
V = 9,600
Step 4: Add to find the total volume:
V = 150 + 9, 600
V = 19,350
The combined volume is 19, 350 cubic centimeters.
Example 2:
How can Ria find the volume of the china cabinet. Find the height of the top section of the china cabinet? Find the volume of the cabinet?
![Example 2:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/580b93c6-a53d-4a79-a3f5-abcb6737836b.png)
Solution:
Step 1: Total height of the cabinet is 7 ft
Bottom part of cabinet height is 3 ft.
Top part of cabinet height is 7 – 3 = 4 ft
Step 2: Find top part of cabinet volume
V = l × w × h
V = 4 × 1 × 4
V = 16
Step 3: Find bottom part of cabinet volume.
V = l × w × h
V = 4 × 2 × 3
V = 24
Step 4: Add two volumes.
V = 16 + 24
V = 40 cubic feet
Volume of China cabinet is 40 cubic feet.
Example 3:
A book is 19 cm wide, 26 cm long and 2 cm thick. There are 8 similar books placed opposite to the top of each other. Find the volume taken up by them.
![Example 3](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7335.png)
![Example 3](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7336.png)
Solution:
Step 1: Find the volume of Book using below formula.
V = l × w × h
Step 2: Find the volume of one book.
![Step 2](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7335.png)
V = 19 × 26 × 2
V = 988 cubic centimeters.
Step 3: We want 8 books volume
![Step 3:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7336.png)
V = 8 × 988
V= 7, 904 cubic centimeters.
Volume of 8 books is 7,904 cubic centimeters.
Example 4:
Thomas wants to buy a new building. He wants to find the volume of the building. How can he find the total volume of the building?
Step 1: Find the volume of each section.
V = l x w x h
Step 2: Find the volume of back block.
V = 8 × 4 × 10
V = 320
Step 3: Find the volume of front block.
V= 6 x 8 x 4
V = 192
Step 4: Add to find the total volume:
V= 320 + 192
V= 704 cubic meters.
The volume of the building is 704 cubic meters.
Example 5:
A cargo company is planning to build two adjacent buildings, which are in the shape of a rectangular prism. They want to construct a metal roof inside the building. Find the volume of the space required to construct the metal roof.
![Example 5:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7337.png)
Step 1: Find the volume of each section.
V = l x w x h
Step 2: Find the volume of back block of the wing.
V = 50 x 50 x 10
V= 25, 000
Step 3: Find the volume of front block of the wing.
V= 75 x 57 x 14
V = 59, 850
Step 4: Add to find the total volume:
V= 25, 000 + 59, 850
V= 84, 850 cubic meters.
The volume of the wings is 84, 850 cubic meters.
Exercise
- Lenin building was designed to have a long first floor with a tower in the middle extending to higher floors, as seen in the image. Find the volume of the building.
![exercise 1](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/11-14.png)
- A box has a length of 7 centimeters, a width of 5 centimeters, and a height of 8 centimeters. What is the volume of the box?
- Stanli is using this box to pack books. He needs to know the volume so he can figure out how many books to pack. Find the volume.
![exercise 3](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/12-16.png)
- Bob has a rectangular prism gift box what it the volume of bobs gift box?
![exercise 4](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/13-9.png)
- Find the volume of below image.
![exercise 5](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/11-15.png)
- The figure shows two right rectangular prisms.
![exercise 6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/12-17.png)
- If the volume of the yellow section is 10 cm? and the volume of the blue section is 12cm’, Find the volume of the figure?
- A crate with dimensions 20 inches wide, 20 inches long, and 12 inches high. What is the
volume of crate? - A compost container measures 4 feet long, 3 feet wide, and 2 feet high. Find the volume
of the compost container. - A box is in the shape of a rectangular prism and has a volume of 360 cubic inches. The
box has a width of 6 inches and a length of 10 inches. What is the height of the box?
Concept Map
![Concept Map](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7340-1024x536.png)
What have we learned
- Understanding the volume.
- How to find volume of rectangular prism using the formula (V) =1 x b x h.
- How to find word problems involving volume?
- How to break rectangular prism into two rectangular prisms?
- How to add two rectangular prism volumes.
Related topics
Addition and Multiplication Using Counters & Bar-Diagrams
Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]
Read More >>Dilation: Definitions, Characteristics, and Similarities
Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]
Read More >>How to Write and Interpret Numerical Expressions?
Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]
Read More >>System of Linear Inequalities and Equations
Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]
Read More >>Other topics
![demo](https://a.storyblok.com/f/128066/544x376/641160f2e6/learn_toast.webp)
Comments: