Finding the Volume of Rectangular Prisms 5.MD.C.5.

Finding the Volume of Rectangular Prisms

5.MD.C.5

Here is a rectangular prism. Let’s find the volume—or the amount of space—inside this prism.We will use this unit cube to help measure volume. How many unit cubes will fill this shape?345678910111213141516171812

18 cubic units

The volume of this shape is 18 cubic units.


Let’s find the volume of this shape by counting unit cubes.2468We can see that one group of 8 unit cubes fills the base of the rectangular prism.Now, there are 2 groups of 8. How many cubes is that?Now, there are 3 groups of 8. How many cubes are there now?The volume of this shape is 24 cubic units.

24 cubic units

1624


If we look carefully at rectangular prisms—like this one—we can tell that there are congruent layers.3 x 6 = 18. So, there are 18 unit cubes here.This prism has 3 layers, and each layer has 6 unit cubes.


The volume of this rectangular prism is 18 cubic units.

18 cubic units


This rectangular prism also has congruent layers.4 x 4 = 16. So, there are 16 unit cubes here.This prism has 4 layers, and each layer has 4 unit cubes.


The volume of this rectangular prism is 16 cubic units.

16 cubic units


Let’s find the volume of this rectangular prism by building an identical one next to it.The base has 6 unit cubes.Here are 2 layers of 6 …3 layers of 6 …… and 4 layers of 6. Now, the prisms are identical. What is 4 x 6?24So, the volume of the prism is 24 cubic units.

24 cubic units


Let’s find the volume of this rectangular prism by building an identical one next to it.The base has 4 unit cubes.Here are 2 layers of 4 …3 layers of 4 …4 layers of 4 …20

20 cubic unitsSo, the volume of the prism is 20 cubic units.… and 5 layers of 4. Now, the prisms are identical. What is 5 x 4?


Let’s find the volume of a rectangular prism by taking apart an identical one and counting the cubes.123467588 x 2 = 168 x 3 = 248 x 4 = 32

32 cubic unitsSo, the volume of this prism is 32 cubic units.


Let’s take apart a copy of this prism to find its volume.3699 x 2 = 189 x 4 = 369 x 5 = 459 x 3 = 27

45 cubic unitsSo, the volume of this prism is 45 cubic units.


52

6 5 × 2 × 6 = 60

Another way to find the volume of a rectangular prism is to multiply its length by its width by its height.How many cubes can we count across the front of the prism?5 — the length of this prism is 5.How many cubes are along this edge?2 — the width of the prism is 2.How many cubes high is the prism?6 — the height of the prism is 6.To find the number of unit cubes, we can multiply the length by the width by the height.What is 5 x 2 x 6?60

60 cubic units

So, the volume of this prism is 60 cubic units.


42

4 4 × 2 × 4 = 32

This prism has a length of 4 …… a width of 2 …… and a height of 4.We can find the volume by multiplying the length by the width by the height.What is 4 x 2 x 4 equal to?32So, this prism has a volume of 32 cubic units.

32 cubic units


33

6 3 × 3 × 6 = 54

This prism has a length of 3 …… a width of 3 …… and a height of 6.We can find the volume by multiplying the length by the width by the height.What is 3 x 3 x 6 equal to?So, this prism has a volume of 54 cubic units.

54 cubic units

54



Lightning Round

How many cubic units are there?

24 cubic units


50 cubic units



27 cubic units



Closing Question


20 cubic units



Finding the Volume of Rectangular Prisms 5.MD.C.5.

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