Volume of Rectangular Pyramids

NEED

DO

VOICE LEVEL 0.
Complete WARM UP
(Question on the
board). Use the
mini whiteboard to
write your answer.

THEN

Be ready to share
your responses to
class.

03.19.2024 WARM UP

Calculate the volume of each
cube.

1.

2.

3. A cube that has a base area of

144 mm2 and a height of 12 mm.

Volume of Rectangular Pyramids

March 19, 2024

Grade 7
Accelerated

Mathematics

11

LO:SWBAT solve problems involving the
volume of rectangular pyramids.

DOL: Given a set of problems, students will
correctly solve problems involving the
volume of rectangular pyramids in at least 4
of 5 questions.

7.9A solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids.

12

Lesson Vocabulary

Volume

Rectangular Pyramid

V= Bh

x Base
area

1
3

1
3
xheight

cubic units

14

You have learned about the volume of rectangular prisms.
Today we we look at rectangular pyramids.

What shape is the figure?

What other

shapes does a

rectangular

pyramid have?

Open Ended

What shape is the figure?

What other figures does a rectangular pyramid have?

Use the following sentence stems:

The shape of the figure is....

The other figures are...

15

Now, let’s explore the volume of a rectangular pyramid.
A rectangular prism with dimensions 2 cm by 2 cm by 3 cm
has a volume of 12 cm3. A rectangular pyramid with the same
dimensions has a volume of 4 cm3

How are their

volumes related?

2 cm

2 cm

3 cm

2 cm

2 cm

3 cm

16

Are all the volumes of rectangular pyramids of a prism?
Watch to see our theory in action.

What do you notice?

1
3

17

It’s concluded. The formula for the volume of a rectangular
pyramid is below.The animation shows again the relationship.

B = base area

h = height of the figure

V = Bh

1
3

18

The formula for the volume of a rectangular prism has two
variables. One is capital and one is lowercase.

What is the shape of the base?

What is the formula for base area?

B = base area

h = height of the figure

V = Bh

1
3

19

Here is an example.

Solve for volume using V= Bh

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the height
of the figure, h.

1
3

4 cm
6 cm

4 cm

Note: Multiplying by is
the same as dividing by 3.

1
3

Reorder

Reorder the following steps for solving a volume problem given a picture of the figure:

• Write the formula.

• Identify the base. Replace B with the formula for base area.

• Identify the height of the figure, h.

• Plug in your values and solve.

1

2

3

4

• 1
• 2
• 3
• 4

20

Solve for volume using V= Bh

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the height
of the figure, h.

1
3

1.5 cm

4 cm

6 cm

Now your turn.

Math Response

What is the volume?

Type answer here

Correct Answer: 12

Deg^°

Rad

21

Solve for volume using V= Bh

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the height
of the figure, h.

1
3

2 in
6 in

2.5 in

Math Response

Type answer here

Correct Answer: 10

Deg^°

Rad

Let’s review the activity.

What’s the only difference
when solving for volume of

a rectangular pyramid
versus a rectangular

prism?

22

Open Ended

What’s the only difference when solving for volume of a rectangular pyramid versus a rectangular prism?

Use the following sentence stem: The only difference is.....

The dimensions of a rectangular pyramid are

6 cm by 2.5 cm by 3 cm. What is the volume of
the rectangular pyramid in cubic centimeters?

Tip: The base
numbers are
the first two.
Draw your
own prism.

Can you solve for volume given only words?

2.5 cm
6 cm

3 cm

23

Some of the dimensions of a rectangular pyramid

are shown below. The height of the pyramid is

4 cm. What is the volume of the rectangular

pyramid in cubic centimeters?

What’s unique about this problem?

1.5 cm

5 cm

Some of the dimensions of a rectangular pyramid

are shown below. The height of the pyramid is

4 cm. What is the volume of the rectangular

pyramid in cubic centimeters?

4 cm

24

A pyramid and it’s dimensions are shown below.

Jordan solves for the volume and shows his work.

Is he correct?

25

9 cm

5 cm

10 cm

Open Ended

Is Jordan correct?

Use the following sentence stem:

Jordan is correct because.....

Jordan is incorrect because.....

A rectangular pyramid has a height of 12 inches
and a base area of 20 in2. What is the volume

of the rectangular pyramid in cubic inches?

A. 32 in3

B. 240 in3

C. 80 in3

D. 1,600 in3

26

Can you solve for volume given only two numbers?

Multiple Choice

A rectangular pyramid has a height of 12 inches and a base area of 20 in².

What is the volume of the rectangular pyramid in cubic inches?

• 32 in³

• 240 in³

• 80 in³

• 1,600 in³

A birdhouse came in two parts and

are shown below.

What is the combined volume of the

two pieces in cubic inches?

What’s unique about this problem?

6 in

9 in

4 in

8 in

A birdhouse came in two parts and

are shown below.

What is the combined volume of the

two pieces in cubic inches?

27

28

Solve for the height if the volume is 48 ft3.

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the
dimensions you know.

What’s different?

2 in

6 in

?

29

Solve for the height if the volume is 40 ft³.

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the
dimensions you know.
4 in

5 in

?

Math Response

Solve for the height if the volume is 40 ft3.

Type answer here

Correct Answer: 6

Deg^°

Rad

A rectangular pyramid has a volume of 120 cm3
and a base area of 15 cm2. What is the height of

the pyramid in inches?

Can you solve for any dimension given only two numbers?

30

?

15 cm2

Tip: Is the base
area divisible

by 3?

A rectangular pyramid has a volume of 64 in3
and a height of 16 in. What is the base area of

the rectangular pyramid in inches?

A. 4 in2

B. 48 in2

C. 12 in2

D. 1,024 in2

31

Can you tell from the answer choices what you are solving for?

16 cm

?

The associative property of

multiplication is used in Step B.

Could you divide by 3

in Step A instead?

Why? How might this

help?

Yes. 6 is divisible by 3.

It might help dividing the smaller
number then multiplying them all.

32

B

A