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Lesson 14: Volume of Pyramids
7.G.6
Math Mission:
•
Things to be mindful of?
•
How is this assessed?
Vocabulary
•
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I will discover the formula for finding
the volume of a pyramid and apply
the formula to solve problems during
Work Time (which may include
exploring animations, comparing
formula of different prisms, and/or
finding volume of real-world
pyramids) and earn a proficient
score on my exit slip.
Multiplying by 1/3 is the same as
dividing by 3.
Slicing a pyramid
Pyramid
DONOW –
1). What is the volume of the triangular prism if the height of the prism is 6 m?
2). What is the volume of the regular hexagonal prism if the height of the prism is
10m?
Key Concepts:
1). The volume of a pyramid is one-third the volume of a prism with the same base
and height.
Type of Pyramid
Triangular
Drawing
Shape of Base
Volume
Square
Pentagonal
2). The shape of the base does not matter (including if it’s a circle).
Goals and Learning Objectives:
1). Formula for the volume of a pyramid.
!
Volume = ! x base x height
2). Apply the volume formula to solve problems.
Lesson 14: TRIAL
Gabriel is helping his mother build a sand sculpture at the beach in the shape of a
pyramid. The square pyramid has a base with a length and width of 12 inches each
and a height of 14 inches.
1. (ORANGE) Label the dimensions of the sand sculpture on the square pyramid
below.
2). (YELLOW) What is the area of the base of the pyramid?
3). (GREEN) What is the volume of the square pyramid?
For each question you missed you must:
1). Answer the writing prompts in detail 3-4 complete sentences.
2). Make a connection to the Work Time problem 2-3 complete sentences.
Missed
Question
Orange
Yellow
Green
Writing Prompt
“The mistake that I made, was that …
But now I know … For example …”
I didn’t know how to label the
dimensions of the pyramid.
I did not attempt to solve the problem
and therefore need to answer all of
the prompts above.
I didn’t know what the polygon base
of the pyramid was.
I didn’t know how to find the area of
the polygon base.
I did not attempt to solve the problem
and therefore need to answer all of
the prompts above.
I didn’t multiply the area of the
polygon base by the height of the
pyramid.
I did not attempt to solve the problem
and therefore need to answer all of
the prompts above.
Connection to Work Time
Discuss the connection
between the TRIAL
question and your work
completed during work
time.
Pearson Digital Agenda Unit 4 – Lesson 14: Volume of Pyramids
Work Time – Slide #5 Find the
Volume of the Great Pyramid
in Egypt
The Great Pyramid in Egypt is
about 480 feet high. It has a
square base with side lengths
of about 750 feet.
1). What is the volume of the
pyramid?
A rectangular prism has a
height of 9 cm, a width of 4
cm, and a length of 2 cm.
2). Find the dimensions of a
rectangular pyramid that has
the same volume as the prism.
3). Can you find more than
one solution?
Work Time – Slide #4 Find Opening – Slide #1
Volumes of Rectangular Shape Animation
Right Pyramids
Watch the video.
1). What is the formula
for the volume of a prism 1). What does this video
(with any type of base)? show?
2). Use the formula from
#1 to determine the
formula for the volume
of a right rectangular
pyramid.
2). What can you say
about the volume of a
pyramid based on the
video?
Work Time – Slide #3
3). What is the volume of Find Volumes of Right
a right rectangular
Pyramids
pyramid that has a
height of 8 in and a
Watch the video.
base that is 5 in long
and 6 in wide?
1). What does the video
demonstrate?
Course 2 Volume 2 pg.
657 #1-8
2). How does the video
relate to the video in
Slide #1?
3). If the pyramid and
cube had different
heights or widths from
each other, do you
think the results would
be different?
4). If the base of the
prism had a different
shape, do you think the
results would be
different?
5). Explain the
difference between
finding the volume of a
prism and finding the
volume of a right
pyramid. Provide
rationale.
Ways of Thinking – Make Connections
Student Names: _________________________________________________
A rectangular pyramid has a volume of 1,560 cubic inches. What is the height of the
pyramid given the base is 13 inches by 15 inches? Use a drawing to model your
pyramid. Explain how you found your answer.
Ways of Thinking – Make Connections
Student Names: _________________________________________________
A rectangular pyramid has a volume of 160 cubic feet. Find two possible sets of
measurements for the base area and height of the pyramid. Use a drawing to
model your pyramid. Explain how you found your answer.
Ways of Thinking – Make Connections
Student Names: _________________________________________________
Explain why it is important to know the shape of the base of a pyramid when finding
the volume of the pyramid. Use a drawings to model your pyramids.
Summary of the Math
à The volume of a pyramid is one-third the volume of a prism with the same base
and height, regardless of the shape of the base.
!
à The formula for the volume of a pyramid is Volume = ! x base x height
Reflection (www.msmallett.weebly.com)
"The difference between finding the volume of a rectangular
and pyramid prism is ..." Exit Slip
The table shows the base dimensions and heights of 4 rectangular pyramids. Sort the
pyramids from least to greatest volume.
Pyramids
A
B
C
D
L (feet)
4
6
5
3
W (feet)
9
6
5
6
Which pyramid has the greatest volume? Show all your work.
H (feet)
5
7
9
12