Solve Word Problems Using Volume

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. 

Word problems involving volume 

Jerimia built a house out of building blocks. Find the volume of the house Jerimia built. 

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? 

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. 

Solution: 

Step 1: Find the volume of Book using below formula. 

V = l  × w  × h  

Step 2: Find the volume of one book. 

V = 19 × 26 × 2 

V = 988 cubic centimeters. 

Step 3: We want 8 books volume 

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. 

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.

• 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.

• Bob has a rectangular prism gift box what it the volume of bobs gift box?

• Find the volume of below image.

• The figure shows two right rectangular prisms.

• 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 

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.