# 10.15: Volume of Prisms Using Unit Cubes

**At Grade**Created by: CK-12

**Practice**Volume of Prisms Using Unit Cubes

Remember Jillian's box from an earlier Concept?

Jillian is working on her special box and is wondering how much she can fit inside of it. The box is a rectangular prism and has the following dimensions: 7" x 6" x 4".

Can you use unit cubes to figure out the volume of the box? How?

**This Concept is about identifying volume. You will learn one strategy for accomplishing this task.**

### Guidance

In this Concept, we will look at the ** volume** of prisms.

**Volume is the amount of space inside a solid figure**.

In this Concept, we will look at the volume of prisms.

**These cubes make up a rectangular prism. The cubes represent the volume of the prism.**

This prism is five cubes by two cubes by one cube. In other words, it is five cubes long, by two cubes high by one cube wide.

We can multiply each of these values together to get the volume of the rectangular prism.

5 \begin{align*}\times\end{align*}

If we count the cubes, we get the same result.

**The volume of the rectangular prism is 10 cubic units or units\begin{align*}^3\end{align*} 3.**

Identify the volume of each prism.

#### Example A

**Solution: 10 cubes**

#### Example B

**Solution: 16 cubes**

#### Example C

**Solution: 9**

Now back to Jillian's box. Here is the original problem once again.

Jillian is working on her special box and is wondering how much she can fit inside of it. The box is a rectangular prism and has the following dimensions: 7" x 6" x 4".

Can you use unit cubes to figure out the volume of the box? How?

If you noticed in the three examples above, each measurement indicated the number of unit cubes that would be needed. We can apply this to Jillian's box.

There are seven 1 inch cubes for the length.

There are six 1 inch cubes for the width.

There are four 1 inch cubes for the height.

\begin{align*}7 \times 6 \times 4 = 168\end{align*}

**Jillian's box will hold 168 unit cubes.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Surface area
- the outer covering of a solid figure-calculated by adding up the sum of the areas of all of the faces and bases of a prism.

- Net
- diagram that shows a “flattened” version of a solid. Each face and base is shown with all of its dimensions in a net. A net can also serve as a pattern to build a three-dimensional solid.

- Triangular Prism
- a solid which has two congruent parallel triangular bases and faces that are rectangles.

- Rectangular Prism
- a solid which has rectangles for bases and faces.

- Volume
- the amount of space inside a solid figure

### Guided Practice

Here is one for you to try on your own.

What is the volume of this figure?

**Answer**

How many cubes are in this figure? We can see that if we count all the cubes, that we have 48 cubes.

**The volume of this prism is 48 cubic units or \begin{align*}\text{units}^3\end{align*} units3.**

### Video Review

Here is a video for review.

Khan Academy: Solid Geometry Volume

### Practice

Directions: Find the surface area and volume of each prism.

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10

Directions: Identify each type of prism.

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Net

A net is a diagram that shows a “flattened” view of a solid. In a net, each face and base is shown with all of its dimensions. A net can also serve as a pattern to build a three-dimensional solid.Rectangular Prism

A rectangular prism is a prism made up of two rectangular bases and four rectangular faces.Surface Area

Surface area is the total area of all of the surfaces of a three-dimensional object.Triangular Prism

A triangular prism is a prism made up of two triangular bases and three rectangular faces.Volume

Volume is the amount of space inside the bounds of a three-dimensional object.### Image Attributions

Here you'll learn to identify the volume of prisms using unit cubes.