## 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.

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