Finding the Volumeof Irregular Shapes

5.MD.C.5

Here is a prism that is not rectangular.We can find its volume by counting the number of unit cubes needed to completely fill it.1234510152025The volume of this shape is 25 cubic units.

25 cubic units

Finding the Volume of Irregular Shapes

Let’s find the volume of this prism by building an identical copy.1234566 x 2 = 126 x 3 = 186 x 4 = 24The volume of this shape is 24 cubic units.

24 cubic units

Finding the Volume of Irregular Shapes

We can also find the volume of a prism by subtracting cubes.Here is an exact copy of the prism. Let’s subtract and count unit cubes.12345672 sets of 7 is 14.3 sets of 7 is 21.And, 4 sets of 7 is 28.The volume of this prism is 28 cubic units.

28 cubic units

Finding the Volume of Irregular Shapes

Let’s build a copy of this prism to find its volume.24681020304050The volume of the prism is 50 cubic units.

50 cubic units

Finding the Volume of Irregular Shapes

23

5

22

5

20 30 50

50 cubic units

Another way to find the volume of an irregular prism is to decompose it into rectangular prisms.Now, let’s find the volume of each prism. Then, we can add them together.The first prism has a length of 2 …… a width of 2 …… and a height of 5. So, how many unit cubes make up the first prism?20The second prism has a length of 2 …… a width of 3 …… and a height of 5. So, how many unit cubes make up the second prism?How many unit cubes are there in all?50

+ =30

Finding the Volume of Irregular Shapes

50 cubic units

This prism has a volume of 50 cubic units.

Finding the Volume of Irregular Shapes

Here is another prism that is not a rectangular prism.

Finding the Volume of Irregular Shapes

But, we can break it into multiple rectangular prisms.

Finding the Volume of Irregular Shapes

52 cubic units

22

4

163

2

2

122

2

6

24+ + = 52Let’s separate the rectangular prisms.Now, we can find the volume of each part.How many units cubes make up the first prism?16How many units cubes make up the next prism?12How many units cubes make up the last prism?24Now, what is the sum of all the unit cubes?52The entire volume is 52 cubic units.

Finding the Volume of Irregular Shapes

52 cubic units

Now, let’s put the prisms back together.

Finding the Volume of Irregular Shapes

52 cubic units

The volume of this prism is 52 cubic units.

Finding the Volume of Irregular Shapes

Here is another shape that has volume, but is not a rectangular prism.Let’s break it into rectangular prisms.

Finding the Volume of Irregular Shapes

36 cubic units

2

4

3

24

11

4

4

22

2

8+ + = 36Now, let’s find the volume of each part.How many units cubes make up the first prism?24How many units cubes make up the next prism?4How many units cubes make up the last prism?8Now, what is the sum of all the unit cubes?36The entire volume is 36 cubic units.

Finding the Volume of Irregular Shapes

36 cubic units

Now, let’s put the prisms back together.

Finding the Volume of Irregular Shapes

The volume of this shape is 36 cubic units.

36 cubic unitsFinding the Volume of Irregular Shapes

Finding the Volume of Irregular Shapes

Lightning Round

How many cubic units are there?

15 cubic units

Finding the Volume of Irregular Shapes

10 cubic units

How many cubic units are there?

Finding the Volume of Irregular Shapes

34 cubic units

How many cubic units are there?

Finding the Volume of Irregular Shapes

Closing Question

Finding the Volume of Irregular Shapes

36 cubic units

How many cubic units are there?

Finding the Volume of Irregular Shapes