Volume of Similar Figures - Granite School District

LESSON PLAN (Linda Bolin)
Lesson Title: Finding Volume of Similar Figures
Course: Pre-Algebra Date Feb Lesson 4
Utah State Core Content and Process Standards:
4.2b Explain that if a scale factor describes how corresponding lengths in two similar
objects are related, then the cube of the scale factor describes how the
corresponding volumes are related.
4.2c Find volumes of similar figures, using the scale factor
Lesson Objective(s): Identify the relationship between the corresponding sides in two
similar figures and their volumes. Find volumes of similar figures.
Enduring Understanding (Big Ideas): Essential Questions:
Indirect measures for similar figures • How can we describe the relationship between
the corresponding sides of similar figures and
their volumes?
• How can this relationship help us determine the
Skill Focus:
Use the relationship between
corresponding sides of similar figures to
find volume.
volume for similar figures?
Vocabulary Focus:
Corresponding sides, similar figures, volume
Materials:
• Linker cubes for each team
• Scissors, card stock, tape, Jenga game (optional activity)
• Worksheets: Investigating Similar Figures, Volumes of Similar Figures, Scale Factors and
Volume With Linking Cubes, Jenga Game
Assessment (Traditional/Authentic): Performance task, observation of student groups,
questions
Ways to Gain/Maintain Attention (Primacy):
Manipulatives, cheer, games, foldable
Written Assignment:
• Worksheets: Investigating Similar Figures, Volumes of Similar Figures, Scale Factors and
Volume With Linking Cubes, Jenga Game
• Journal: Foldable-Scale Factor for Finding Area and Volume of Similar Figures
Post Vocabulary on the board
Content Chunks
Starter:
4.5 cm
A
C
4 cm
B
D
1. Find the area of rectangle ABCD
2. These rectangles are similar. What is the scale
factor?
E
F
3. Use the scale factor to find the area for the
larger rectangle
9 cm 4. Write 3, 200,000 using scientific notation
G
H

Lesson Segment 1: How can we describe the relationship between the
corresponding sides of similar figures and their areas?
Give each team of students 100 linking cubes. They will be building similar prisms and
comparing the ratio of corresponding sides to the ratio of the volumes. Work with
them to build prisms as they complete the “Investigating Similar Figures, Scale Factors
and Volume With Linking Cubes” investigation worksheet. If they have difficulty
building a rectangular prism, remind them to first build the base by forming lw, and
then stack the number of layers for h.
As they work together in small groups, ask them to rotate roles: Builder (handles the
cubes), Coach (tells builder how it should look and suggest ideas for building),
Draftsman (reminds all to sketch the prisms helping each of them with the drawing),
Encourager (makes sure there are no put-downs and that each person is taking a turn
with the roles). Have students build and sketch, and discuss the answers to the
questions as a class.
Predicting and testing the hypotheses: Remind students that in the last lesson,
when finding area (or the number of squares needed to cover a similar figure), they
used the scale factor squared. Ask students to predict what might happen with the
scale factor when finding volumes of similar figures. Have them look for a pattern that
relates the scale factor to the number of cube units in each prism. Make sure student
focus on the relationship between the scale factor and the new volume. They should
begin to see that the units of volume in the larger figure are always the original volume
multiplied by the cube of the scale factor. When they write the ratio for each make this
explicit: The volume of the larger figure is the cube of the scale factor multiplied by
the volume of the smaller figure. Help them make the connection between volume
being measured in cubed units and the scale factor being cubed when finding the
volume of the larger prism.
Lesson Segment 2: How can the relationship between volumes of similar
figures help us find missing areas?
Teach the students the following cheer. Have them compare this cheer to the cheer for
area from the last lesson. How are the procedures the same? Different?
Similar figures? I don’t cry.
I can find volume if I try.
Cube the scale factor and multiply
By the smaller volume! My oh My!
Similar figures? I’m not scared!
I’ll find area if I’m dared.
Multiply the scale factor squared
By the smaller area-I’m prepared!

Play Lie Detector again for completing the worksheet, Volume of Similar Figures.
Materials: Give each small group a Smart Pal with blank paper or large team board and
marker
Procedure: Divide the class into two teams, A and B. Team members work together to
complete one assigned part of the worksheet. Give students a little time to check with
team members and to work the part of the worksheet correctly. The team should then
decide if they are going to tell a lie or tell the truth. If they choose to tell the truth, a
scribe writes the responses to the worksheet correctly on the Smart Pal or Team Board.
If they decide to tell a lie, the scribe writes part of their response incorrectly on the
Smart Pal or team board. Teacher selects one person from team A to be The
Presenter. The Presenter stands in the front of the room shows the team board and
explains what was done (either telling the truth, or telling a lie about the problem).
The class is given a little time to discuss the response in small groups. The Presenter
then chooses one person from Team B to be the Lie Detector and to tell whether they
believe the explanation was truth or lie. If The Lie Detector thinks the explanation was
a lie, he/she has to explain where the lie occurred and correct it. If the Lie Detector is
correct, Team B gets a point. If not, The Presenter tells whether their explanation was
the truth or a lie. If it was a lie, The Presenter tells why. The game proceeds with
each team taking a turn to be Presenter and Lie Detector.
Journal:
Students should make the foldable and fill in the blanks to show each step.
Application review of the affect of scale factor on length, area, and volume.
Have student play Jenga as described on the attached worksheet.

Investigating Similar
Figures, Scale Factors and
Volume With Linking Cubes
Name____________________________
Date _______
Use linking cubes to build the two
similar prisms for each problem. Count
the volume (cubes) for each. Fill in the blanks.
1. Build a cube with side length of 1. Sketch it here.
Build a similar figure using a scale factor of 2. Sketch it here.
Volume of smaller cube _____. Volume of larger cube _____.
What is the value of the scale factor³?_____.
What is the ratio of the larger cube’s volume to the smaller cube’s volume ______.
2. Build a cube with side length of 2. Sketch it here.
Build a similar figure using a scale factor of 2. Sketch it here.
Volume of smaller cube _____. Volume of larger cube _____.
What is the value of the scale factor³?_____.
What is the ratio of the larger cube’s volume to the smaller cube’s volume ______.
3. Build a prism with dimensions l =1, w =2, h =2. Sketch it here.
Build a similar figure using a scale factor of 2. Sketch it here.
Volume of smaller prism _____. Volume of larger prism _____.
What is the value of the scale factor³?_____.
What is the ratio of the larger prism’s volume to the smaller prism’s volume ______.

4. Build a cube with side length of 1.
Build a similar figure using a scale factor of 3. Sketch it here.
Volume of smaller cube _____. Volume of larger cube _____.
What is the value of the scale factor³?_____.
What is the ratio of the larger cube’s volume to the smaller cube’s volume ______.
5. Build a cube with side length of 2. Sketch it here.
Build a similar figure using a scale factor of 3. Sketch it here.
Volume of smaller cube _____. Volume of larger cube _____.
What is the value of the scale factor³?_____.
What is the ratio of the larger cube’s volume to the smaller cube’s volume ______.
6. Build a prism with dimensions l =1, w =2, h =2. Sketch it here.
Build a similar figure using a scale factor of 3. Sketch it here.
Volume of smaller prism _____. Volume of larger prism _____.
What is the value of the scale factor³?_____.
What is the ratio of the larger prism’s volume to the smaller prism’s volume ______.
7. How does the scale factor compare to the ratio of the volumes?
8. If you build two similar cubes with a scale factor of 4, what would you expect the
ratio of their volumes to be? Explain your answer.

Volumes of Similar Figures
Name _____________________
Date____
Each set of three figures below are similar within the set.
1. Fill in the blanks for the missing measurements in prism B and prism C. What is the
scale factor for prism B ____ ? For prism C_____?
A) B) C)
4 8 ___?
2
3 4
___? 6
9
2. Find the volume for prism A, and then find the volume for Prism B and for C using
the scale factor for each.
A) B) C)
3. Fill in the blanks for the missing measurements prism E and prism F. What is the
scale factor for prism E ____ ? For prism F____?
D) E) F)
2
2
2 6 ___?
___?
6 10
10
4. Find the volume for prism D, and then find the volume for Prism E and for F using
the scale factor for each.
D) E) F)

5. Fill in the blanks for the missing measurements for cylinder H and cylinder I. What
is the scale factor for cylinder H ____ ? For cylinder I____?
G) H) I)
4
2 16 ___?
___?
10
6. Find the volume for prism G, and then find the volume for Prism H and for I using
the scale factor for each.
G) H) I)
K) Explain the relationship between the scale factor and the volume of two similar
figures.
L) Complete the table below for the given dimensions and scale factors of the similar
figures described.
Dimensions of a
smaller figure
Volume of the
smaller figure
Scale factor
for a larger
figure
Rectangular prism:
l = 3, w = 5, h = 4 4
Cube:
S = 5 3
Cylinder:
r = 3, h = 10 2
Rectangular prism:
l = 8, w = 2.5, h = 4 5
Cube:
S = 4 2
Cylinder:
r = 6, h = 5 3
Volume for larger
figure

Scale Factor For
Finding Area
Of Similar Figures
Scale Factor For
Finding Volume
Of Similar Figures

5
?
2
4
To find the area of the larger figure, follow these
steps:
1. Find the scale factor like this _____________
2. Square the scale factor like this ___________
3. Find the area of the smaller figure like this
____________________
4 Multiply the squared scale factor by the small
area like this ________________________
4
2
?
3
?
6
To find the volume of the larger figure, follow
these steps:
1. Find the scale factor like this _____________
2. Cube the scale factor like this ___________
3. Find the volume of the smaller figure like this
____________________
4 Multiply the cubed scale factor by the small
volume like this ____________________

TEAM JENGA HOW MANY JENGAS CAN YOU BUILD?
Name____________________
You will need: scissors, tape, ruler, a small piece of card stock and a large piece
of card stock or construction paper.
1. Sketch your Jenga block (also known as a rectangular prism.)
2. Using the small paper, make a net for
the Jenga block (wrapping all the
surfaces). Sketch the net for the Jenga.
3. How many lateral faces are there? ____ How many bases are there? ____
4. Measure the length, width and height of your JENGA (in centimeters)
Length =_______ Width = ________ Height = _________
5. Find the volume of your Jenga. (see class reference sheet for formula)
6. Find the surface area of your Jenga block (see reference sheet)
7. If the Jenga is enlarged using a scale factor of 2, what will the dimensions
of the larger Jenga be? Length = ________ Width = ________
Height = _________
8. If the Jenga is enlarged using a scale factor of 2, what will the surface
area of the larger Jenga be?
9. Using the large piece of paper, make a net of the larger Jenga.

10. When everyone on your team has finished to # 9, write the time here.
__________. Call your teacher over to initial that all have finished to this
point. _____________. (Teacher initials)
11. As a team it is your job to build from card stock as many of the enlarger
Jengas as possible in 30 minutes. Work together as a team with everyone
contributing to the building.
12. How many congruent Jengas did your team build? _____ (If your Jengas
are not congruent, they will not stack and slide well for playing Jenga.)
Now play Jenga:
As a team, build the highest tower you can build without it toppling over. You
get three tries. Record your heights (levels) for your three tries here:
Round 1____, Round 2____, Round 3 ____
Next, rebuild the next highest tower. Take turns sliding pieces out of the
Jenga without toppling the tower. You get 1 point for each block pulled out
without toppling the tower. You do not get a point for the block that topples
the tower.
Scoring: 1 point for each level in the highest tower + 1 point for each block
removed without toppling the tower.
SCORE HERE:
13. How did each person on your team contribute to the team’s success in the
building?
14. What did you learn from this team project?