CH09-04 lesson

Volume of Composite Figures Learning Activity

A focused Grade 5 learning session for Volume of Composite Figures using visual models, worked examples, strategy guidance, and a short mastery check.

Start the lesson Print practice sample
15
minutes
6
lesson parts
11
practice items
Learning goal

Students will find volume of composite figures by decomposing them into rectangular prisms.

Student goal: I can find volume of composite figures.

Helpful first: Finding Volume Using Formulas
concept

Learn the Idea

Volume of Composite Figures is the Grade 5 skill of students recognize that volume is additive and find the volume of solid figures composed of two non-overlapping right rectangular prisms. They decompose complex figures into simpler parts and add the volumes.

How many equal-sized cubic units fill the solid without gaps or overlaps?

Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.

The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.

  • Think in layers of equal-sized cubes instead of only memorizing a formula.
  • Connect length, width, and height to the number of cubes in each layer.
  • Decide whether the figure can be decomposed into smaller rectangular prisms.
  • Use the topic language from class discussions: Students recognize that volume is additive and find the volume of solid figures composed of two non-overlapping right rectangular prisms. They decompose complex figures into simpler parts and add the volumes.
visual model

See the Math

Visual Model 1

Question: A step-shaped solid is decomposed into three non-overlapping rectangular prisms. The prisms measure \(6\) feet by \(4\) feet by \(3\) feet, \(4\) feet by \(4\) feet by \(2\) feet, and \(3\) feet by \(3\) feet by \(3\) feet. What is the total volume?

Grade 5 Volume of Composite Figures figure 1

  • A. 104 cubic feet
  • B. 131 cubic feet
  • C. 59 cubic feet
  • D. 99 cubic feet

How the model helps: Work one prism at a time: \(6 \times 4 \times 3 = 72\), \(4 \times 4 \times 2 = 32\), and \(3 \times 3 \times 3 = 27\). Add the non-overlapping volumes: \(72 + 32 + 27 = 131\) cubic feet.

worked example

Follow a Worked Example

Example 1

Question: A composite stage platform is made from two non-overlapping rectangular prisms. Prism A is \(4\) centimeters long, \(2\) centimeters wide, and \(2\) centimeters tall. Prism B is \(3\) centimeters long, \(3\) centimeters wide, and \(1\) centimeter tall. What is the total volume?

  • A. 25 cubic centimeters
  • B. 16 cubic centimeters
  • C. 9 cubic centimeters
  • D. 33 cubic centimeters
  1. Find each part first: Prism A is \(4 \times 2 \times 2 = 16\) cubic centimeters, and Prism B is \(3 \times 3 \times 1 = 9\) cubic centimeters.
  2. Because the parts do not overlap, add them: \(16 + 9 = 25\) cubic centimeters.

Answer: 25 cubic centimeters

Example 2

Question: A composite classroom model is made from two non-overlapping rectangular prisms. Prism A is \(5\) inches long, \(4\) inches wide, and \(5\) inches tall. Prism B is \(6\) inches long, \(4\) inches wide, and \(3\) inches tall. What is the total volume?

  • A. 100 cubic inches
  • B. 172 cubic inches
  • C. 72 cubic inches
  • D. 192 cubic inches
  1. Find each part first: Prism A is \(5 \times 4 \times 5 = 100\) cubic inches, and Prism B is \(6 \times 4 \times 3 = 72\) cubic inches.
  2. Because the parts do not overlap, add them: \(100 + 72 = 172\) cubic inches.

Answer: 172 cubic inches

real world

Connect It to a Real Situation

Problem 1

Question: A composite museum stand is made from two non-overlapping rectangular prisms. Prism A is \(7\) meters long, \(4\) meters wide, and \(6\) meters tall. Prism B is \(6\) meters long, \(2\) meters wide, and \(2\) meters tall. What is the total volume?

  • A. 168 cubic meters
  • B. 24 cubic meters
  • C. 220 cubic meters
  • D. 192 cubic meters

Answer: 192 cubic meters

Why it works: Find each part first: Prism A is \(7 \times 4 \times 6 = 168\) cubic meters, and Prism B is \(6 \times 2 \times 2 = 24\) cubic meters. Because the parts do not overlap, add them: \(168 + 24 = 192\) cubic meters.

strategy

Avoid Mistakes and Choose a Strategy

  • Starting the computation before identifying what the numbers, units, or parts represent.
  • Confusing area and volume or forgetting that volume is measured in cubic units.
  • Forgetting to estimate, which makes it easier to miss an unreasonable answer.
  • Stopping at a number without explaining what the answer means in context.
  • Read the situation slowly and name what each number or label represents.
  • Think in layers of cubes or base-area groups before using a formula.
  • Estimate first so you already know the answer's approximate size.
  • Check the answer with an inverse operation, another representation, or a sentence explanation.
  • Say the math idea out loud in simple words before writing the final answer.
summary

Remember the Key Idea

Volume of Composite Figures gets easier when students read the model, track what each number means, and explain why the answer fits the situation.

GOLDEN RULE

Think in layers of cubic units, then justify the formula with the model.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G5-C07-T07-Q001 About 1 min

A composite stage platform is made from two non-overlapping rectangular prisms. Prism A is \(4\) centimeters long, \(2\) centimeters wide, and \(2\) centimeters tall. Prism B is \(3\) centimeters long, \(3\) centimeters wide, and \(1\) centimeter tall. What is the total volume?

  1. A 25 cubic centimeters
  2. B 16 cubic centimeters
  3. C 9 cubic centimeters
  4. D 33 cubic centimeters
Check answer and explanation

Answer A: 25 cubic centimeters

Find each part first: Prism A is \(4 \times 2 \times 2 = 16\) cubic centimeters, and Prism B is \(3 \times 3 \times 1 = 9\) cubic centimeters. Because the parts do not overlap, add them: \(16 + 9 = 25\) cubic centimeters.

G5-C07-T07-Q002 About 1 min

A composite classroom model is made from two non-overlapping rectangular prisms. Prism A is \(5\) inches long, \(4\) inches wide, and \(5\) inches tall. Prism B is \(6\) inches long, \(4\) inches wide, and \(3\) inches tall. What is the total volume?

  1. A 100 cubic inches
  2. B 172 cubic inches
  3. C 72 cubic inches
  4. D 192 cubic inches
Check answer and explanation

Answer B: 172 cubic inches

Find each part first: Prism A is \(5 \times 4 \times 5 = 100\) cubic inches, and Prism B is \(6 \times 4 \times 3 = 72\) cubic inches. Because the parts do not overlap, add them: \(100 + 72 = 172\) cubic inches.

guided

1 question
G5-C07-T07-Q003 About 1 min

A composite storage display is made from two non-overlapping rectangular prisms. Prism A is \(6\) feet long, \(2\) feet wide, and \(3\) feet tall. Prism B is \(3\) feet long, \(5\) feet wide, and \(5\) feet tall. What is the total volume?

  1. A 36 cubic feet
  2. B 75 cubic feet
  3. C 111 cubic feet
  4. D 123 cubic feet
Check answer and explanation

Answer C: 111 cubic feet

Find each part first: Prism A is \(6 \times 2 \times 3 = 36\) cubic feet, and Prism B is \(3 \times 5 \times 5 = 75\) cubic feet. Because the parts do not overlap, add them: \(36 + 75 = 111\) cubic feet.

practice

5 questions
G5-C07-T07-Q004 About 1 min

A composite museum stand is made from two non-overlapping rectangular prisms. Prism A is \(7\) meters long, \(4\) meters wide, and \(6\) meters tall. Prism B is \(6\) meters long, \(2\) meters wide, and \(2\) meters tall. What is the total volume?

  1. A 168 cubic meters
  2. B 24 cubic meters
  3. C 220 cubic meters
  4. D 192 cubic meters
Check answer and explanation

Answer D: 192 cubic meters

Find each part first: Prism A is \(7 \times 4 \times 6 = 168\) cubic meters, and Prism B is \(6 \times 2 \times 2 = 24\) cubic meters. Because the parts do not overlap, add them: \(168 + 24 = 192\) cubic meters.

G5-C07-T07-Q005 About 1 min

A composite garden block is made from two non-overlapping rectangular prisms. Prism A is \(8\) centimeters long, \(2\) centimeters wide, and \(4\) centimeters tall. Prism B is \(3\) centimeters long, \(3\) centimeters wide, and \(4\) centimeters tall. What is the total volume?

  1. A 100 cubic centimeters
  2. B 64 cubic centimeters
  3. C 36 cubic centimeters
  4. D 116 cubic centimeters
Check answer and explanation

Answer A: 100 cubic centimeters

Find each part first: Prism A is \(8 \times 2 \times 4 = 64\) cubic centimeters, and Prism B is \(3 \times 3 \times 4 = 36\) cubic centimeters. Because the parts do not overlap, add them: \(64 + 36 = 100\) cubic centimeters.

G5-C07-T07-Q006 About 1 min

A composite science fair model is made from two non-overlapping rectangular prisms. Prism A is \(9\) inches long, \(4\) inches wide, and \(2\) inches tall. Prism B is \(6\) inches long, \(4\) inches wide, and \(1\) inches tall. What is the total volume?

  1. A 72 cubic inches
  2. B 96 cubic inches
  3. C 24 cubic inches
  4. D 132 cubic inches
Check answer and explanation

Answer B: 96 cubic inches

Find each part first: Prism A is \(9 \times 4 \times 2 = 72\) cubic inches, and Prism B is \(6 \times 4 \times 1 = 24\) cubic inches. Because the parts do not overlap, add them: \(72 + 24 = 96\) cubic inches.

G5-C07-T07-Q007 About 1 min

A composite bookcase base is made from two non-overlapping rectangular prisms. Prism A is \(4\) feet long, \(2\) feet wide, and \(5\) feet tall. Prism B is \(3\) feet long, \(5\) feet wide, and \(3\) feet tall. What is the total volume?

  1. A 40 cubic feet
  2. B 45 cubic feet
  3. C 85 cubic feet
  4. D 93 cubic feet
Check answer and explanation

Answer C: 85 cubic feet

Find each part first: Prism A is \(4 \times 2 \times 5 = 40\) cubic feet, and Prism B is \(3 \times 5 \times 3 = 45\) cubic feet. Because the parts do not overlap, add them: \(40 + 45 = 85\) cubic feet.

G5-C07-T07-Q008 About 1 min

A composite play structure is made from two non-overlapping rectangular prisms. Prism A is \(5\) meters long, \(4\) meters wide, and \(3\) meters tall. Prism B is \(6\) meters long, \(2\) meters wide, and \(5\) meters tall. What is the total volume?

  1. A 60 cubic meters
  2. B 140 cubic meters
  3. C 130 cubic meters
  4. D 120 cubic meters
Check answer and explanation

Answer D: 120 cubic meters

Find each part first: Prism A is \(5 \times 4 \times 3 = 60\) cubic meters, and Prism B is \(6 \times 2 \times 5 = 60\) cubic meters. Because the parts do not overlap, add them: \(60 + 60 = 120\) cubic meters.

exit

3 questions
G5-C07-T07-Q009 About 1 min

A composite shipping stack is made from two non-overlapping rectangular prisms. Prism A is \(6\) centimeters long, \(2\) centimeters wide, and \(6\) centimeters tall. Prism B is \(3\) centimeters long, \(3\) centimeters wide, and \(2\) centimeters tall. What is the total volume?

  1. A 90 cubic centimeters
  2. B 72 cubic centimeters
  3. C 18 cubic centimeters
  4. D 102 cubic centimeters
Check answer and explanation

Answer A: 90 cubic centimeters

Find each part first: Prism A is \(6 \times 2 \times 6 = 72\) cubic centimeters, and Prism B is \(3 \times 3 \times 2 = 18\) cubic centimeters. Because the parts do not overlap, add them: \(72 + 18 = 90\) cubic centimeters.

G5-C07-T07-Q010 About 1 min

A composite art display is made from two non-overlapping rectangular prisms. Prism A is \(7\) inches long, \(4\) inches wide, and \(4\) inches tall. Prism B is \(6\) inches long, \(4\) inches wide, and \(4\) inches tall. What is the total volume?

  1. A 112 cubic inches
  2. B 236 cubic inches
  3. C 96 cubic inches
  4. D 208 cubic inches
Check answer and explanation

Answer D: 208 cubic inches

Find each part first: Prism A is \(7 \times 4 \times 4 = 112\) cubic inches, and Prism B is \(6 \times 4 \times 4 = 96\) cubic inches. Because the parts do not overlap, add them: \(112 + 96 = 208\) cubic inches.

G5-C07-T07-Q011 About 1 min

A composite stage platform is made from two non-overlapping rectangular prisms. Prism A is \(8\) feet long, \(2\) feet wide, and \(2\) feet tall. Prism B is \(3\) feet long, \(5\) feet wide, and \(1\) feet tall. What is the total volume?

  1. A 32 cubic feet
  2. B 15 cubic feet
  3. C 47 cubic feet
  4. D 63 cubic feet
Check answer and explanation

Answer C: 47 cubic feet

Find each part first: Prism A is \(8 \times 2 \times 2 = 32\) cubic feet, and Prism B is \(3 \times 5 \times 1 = 15\) cubic feet. Because the parts do not overlap, add them: \(32 + 15 = 47\) cubic feet.

Keep the learning path connected
Previous skillFinding Volume Using Formulas Recommended nextSolving Real-World Volume Problems Same strandConverting Measurement Units Same strandSolving Multi-Step Problems with Conversions
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