Guided Practice: Volume | Open Textbooks

How Guided Practice Works

Learn by Doing

In this lesson, you'll solve problems step-by-step. Click to reveal each step, enter your answers, and get instant feedback!

Remember the Formula:

V = l x w x h

Volume = Length x Width x Height

Guided Problem 1: Simple Rectangular Prism

The Toy Box

Marcus has a toy box that is 15 inches long, 10 inches wide, and 8 inches tall. What is the volume of his toy box?

1 Identify the dimensions +

First, let's identify what we know:

Length (l) = inches

Width (w) = inches

Height (h) = inches

Look at the problem statement. The dimensions are given in order: length, width, height.

2 Write the formula +

The formula for volume of a rectangular prism is:

V = l x w x h

Let's substitute our values:

V = 15 x 10 x 8

3 Calculate step by step +

Let's multiply in steps:

First: 15 x 10 =

Then: __ x 8 =

15 x 10 = 150. Then multiply that result by 8.

4 Write the final answer with units +

Don't forget the units! Volume is measured in cubic units.

Volume = cubic inches (in³)

Guided Problem 2: Finding a Missing Dimension

The Storage Container

A storage container has a volume of 360 cubic feet. It is 12 feet long and 6 feet wide. How tall is the container?

1 Identify what we know and what we need to find +

What we know:

Volume (V) = 360 ft³
Length (l) = 12 ft
Width (w) = 6 ft

What we need to find: Height (h) = ?

2 Set up the equation +

Start with the formula: V = l x w x h

Substitute what we know: 360 = 12 x 6 x h

12 x 6 =

So: 360 = ___ x h

3 Solve for h using division +

To find h, we need to "undo" the multiplication.

If 360 = 72 x h, then h = 360 / 72

h = 360 / 72 = feet

Divide 360 by 72. You can think: what number times 72 equals 360?

Guided Problem 3: Composite Shape

The L-Shaped Planter

An L-shaped planter box is made of two rectangular prisms joined together:

Part A: 8 ft long, 3 ft wide, 2 ft tall
Part B: 4 ft long, 3 ft wide, 2 ft tall

What is the total volume of the planter?

1 Find the volume of Part A +

Part A: 8 ft x 3 ft x 2 ft

Volume of Part A = ft³

8 x 3 = 24, then 24 x 2 = ?

2 Find the volume of Part B +

Part B: 4 ft x 3 ft x 2 ft

Volume of Part B = ft³

3 Add the volumes together +

Total Volume = Volume A + Volume B

Total Volume = 48 + 24 = ft³

Independent Practice

Now try these problems on your own!

Problem 1

A fish tank is 24 inches long, 12 inches wide, and 15 inches tall. What is its volume?

Problem 2

A box has a volume of 480 cm³. If it is 10 cm long and 8 cm wide, how tall is it?

Problem 3

A cube has sides of 9 meters. What is its volume?

Problem 4

An L-shaped room has Part A (12 x 10 x 9 ft) and Part B (8 x 6 x 9 ft). What is the total volume?

Problem 5

A rectangular prism has a base area of 35 square inches and a height of 12 inches. What is the volume?

Problem 6

A shipping crate is 5 m x 4 m x 3 m. A 2 m x 2 m x 3 m box is placed inside. How much space remains?

Problem 7

What is the volume of a rectangular prism that is 7 cm long, 5 cm wide, and 11 cm tall?

Problem 8

A pool is 20 m long, 8 m wide, and 2 m deep. How many cubic meters of water can it hold?

What We Practiced

📐

Using the Formula

V = l x w x h for any rectangular prism

🔍

Finding Missing Dimensions

Use division to find unknown values

🧩

Composite Shapes

Break apart, calculate, then combine

📝

Show Your Work

Step-by-step leads to fewer errors

Key Strategy: Always start by identifying what you know and what you need to find. Write out the formula, substitute your values, and solve step by step. Don't forget your units!

Next Steps

Continue to the Word Problems lesson for real-world applications
Review any guided problems where you needed hints
Practice mental math with simple volume calculations
Challenge yourself with multi-step composite shape problems