Volume of Triangular 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.

03.20.2024 WARM UP

Each shape has a height of 10 cm. Calculate
the volume of each shape.

3. A cube that has a base area of
2.5 cm2.

19 cm2

6 cm

8 cm

Volume of Triangular Pyramids

March 20, 2024

Grade 7 Mathematics

3

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

DOL: Given a set of problems, students will
correctly solve problems involving the
volume of triangular 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.

4

Lesson Vocabulary

Volume

Triangular Pyramid

V= Bh

x Base
area

1
3

1
3
xheight

cubic units

5

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

What shape is
the base of the figure?

What other

shapes does a

triangular

pyramid have?

6

Now, let’s explore the volume of a triangular pyramid.
A triangular prism with dimensions 3 cm by 4 cm by 6 cm has
a volume of 36 cm3. A triangular pyramid with the same
dimensions has a volume of 12 cm3

How do the

shapes compare?

How are their

volumes related?

6 cm

3 cm

6 cm

4 cm

3 cm

4 cm

7

Are all the volumes of triangular pyramids of a prism?
Watch the animation.

1
3

What do you

notice?

8

If you look at your reference chart, the formula for the
volume of a triangular pyramid is the same as it is for
rectangular pyramid. Let’s explore.

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

9

A rectangular pyramid with dimensions 3 cm by 4 cm by 6 cm
has a volume of 24 cm3. A triangular pyramid with the same
dimensions has a volume of 12 cm3

How are their

volumes related?

3 cm

6 cm

4 cm

3 cm

4 cm

Multiple Select

Now, let’s explore the volume of a triangular pyramid.

A triangular prism with dimensions 3 cm by 4 cm by 6 cm has a volume of 36 cm³. A triangular pyramid with the same dimensions has a volume of 12 cm³. How are their volumes related?

• 
  They have the same base.

• Their bases are different.

• The pyramid's volume is 1/3 the prism's volume.

• The prism's volume is 1/3 the pyramid's volume.

10

The work for the
volume of two
pyramids with

same dimensions

using V= Bh is

shown.

What do you
notice? How is
the formula the

same but

the volume is
the rectangular

pyramid?

Rectangular

Pyramid
Triangular Pyramid

The B or base

area is
different

1
2

1
3

11

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

Math Response

What is the volume of the triangular pyramid?

Type answer here

Correct Answer: 16

Deg^°

Rad

Math Response

What is the volume of the triangular pyramid?

Type answer here

Correct Answer: 30

Deg^°

Rad

Tip: The height
of the figure is
separate from
the height of
the base.
Draw your
own prism.

A triangular pyramid has a base with a base
of 7.5 in and a height of 10 in. The height of

the figure is 4 in. What is the volume?

Can you solve for volume given only words?

14

7.5 in

4 in

10 in

Math Response

A triangular pyramid has a base with a base of 7.5 in and a height of 10 in. The height of the figure is 4 in. What is the volume?

Type answer here

Correct Answer: 50

Deg^°

Rad

Some of the dimensions of a triangular pyramid
are shown below. The height of the triangular
pyramid is 2.4 cm. What is the volume of the

pyramid in cubic centimeters?
What’s unique about this problem?

15

6 cm

7 cm

Some of the dimensions of a triangular pyramid
are shown below. The height of the triangular
pyramid is 2.4 cm. What is the volume of the

pyramid in cubic centimeters?

2.4 cm

Multiple Choice

Which number is not needed to solve for the volume of the triangular pyramid

• 5 in

• 9.5 in

• 4 in

• 6 in

Multiple Choice

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

• 20 in³

• 60 in³

• 120 in³

• 40 in³

Multiple Choice

What is the volume in cubic inches?

• 228 in³

• 38 in³

• 114 in³

• 57 in³

A triangular pyramid has a height of 11 inches
and a base area of 18 in2. Choose the correct

volume of the rectangular prism in cubic inches.

Tip: Draw
your own
prism.

Can you solve for volume given only two numbers?

18

A. 66 in3

B. 33 in3

11 in

18 in2

Multiple Choice

A triangular pyramid has a height of 15 inches and a base area of 27 in2. What is the volume of the triangular pyramid in cubic inches?

• 135 in³

• 67.5 in³

• 101.25 in³

• 405 in³

3 ft

5 ft

20

Solve for the height if the volume is 30 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 strategy did I use

to solve?

Multiple Choice

A triangular pyramid has a volume of 156 in³ and a height of 12 in.

What is the base area of the triangular pyramid in inches?

• 26 in²

• 13 in²

• 39 in²

• 312 in²