# 7.12 Find volume using unit cubes

Lesson

## Ideas

We have counted squares to  find the area of a shape  and can use that to help us find the volume in this lesson. Let's try this problem to review.

### Examples

#### Example 1

Find the area of the shape below.

Worked Solution
Create a strategy

Count the total number of squares.

Apply the idea

There are 5 squares inside the shape.

\text{ Area }= 5 \text{ units}^2

Idea summary

To find the amount of space a shape takes up, we can use a unit square.

## Volume with unit cubes

This video introduces the unit cube and how it can be used to measure volume (space an object takes up).

### Examples

#### Example 2

In this figure, 1\text{ block}=1\text{ cm}^3. What is the volume of the solid figure?

Worked Solution
Create a strategy

Count the total number of blocks.

Apply the idea

There are 10 blocks in the solid.

\text{Volume}=10\text{ cm}^3

Idea summary

Volume means the amount of space a 3D shape takes up.

To find the volume we can count the number of unit squares that fit inside the shape.

## Volume with arrays

What if you cannot see all the blocks? Can we still work out the volume?

### Examples

#### Example 3

In this figure, 1\text{ block}=1\text{ cm}^3. What is the volume of the solid figure?

Worked Solution
Create a strategy

Multiply the columns by the rows of the array then multiply the answer with the number of sets the solid figure has.

Apply the idea

We can see on the figure that the front face is an array of blocks with 4 rows and 3 columns. We have 2 sets of this face.

Idea summary

If an object is solid, and has no gaps, we can use arrays to count the number of blocks.

We can find the volume of a prism of unit cubes by multiplying the number of rows by columns in the face. Then we multiply the answer by the number of sets of these blocks.