This document provides examples and explanations of volume calculations for various architectural structures from around the world. It includes diagrams of buildings like the Elephant Building in Bangkok and the Longaberger building in Ohio. Readers are walked through calculations of the volume of hummus containers, crooked streets in San Francisco, and the world's steepest staircase in China. The document encourages sharing teaching resources to help one another improve.
3. • Work in pairs
• Brainstorm 3 ways
to improve it
4. Hands-on aspect
Images
Videos
Diagrams
Games
Relating to other disciplines:
Business (economics)
Architecture
Tourism (other countries)
History (other countries)
5. Volume is a very important quantity
It determines how much “stuff” can go into a
container
In-class demonstration
PAPER
ROLLING
EXPERIMENT
6. Consumers want maximum volume for their $
Companies want to minimize volume
Looking at this makes it
look like the hummus is
filled to the bottom,
giving you a lot of
chickpea for your buck…
They show a picture of
the top and sides of the
container…why not the
bottom?
7. Part of the bottom has been
pushed in, to make it contain
less hummus!
Assume the pushed in part is a
hemisphere with radius of 3cm,
and the hummus container has a
radius of 7cm. What percentage
of the total container size is
missing hummus?
HOW MUCH
HUMMUS WE
THINK THERE IS
HOW MUCH
HUMMUS THERE
ACTUALLY IS
8. Architecture from all over the world
Elephant
Building –
(Bangkok,
Thailand)
12. When designing a building, an architect must
measure carefully so the structure is not only
pleasing to the eye, but functions properly
It’s not even just buildings, its roads.
e.g. “The Crookedest Street in the World” in San
Francisco
13.
14. Underneath the street is dirt and rock,
which creates a foundation for the
road. Determine the volume of the
crookedest street assuming a base that
is parallel to level ground.
10 m
60 m
70 m
1. We would model the street at a
triangular based prism
2. Just like a triangle is half the area
of a rectangle, a triangular based
prism is half the volume of a
rectangular prism
Volume =
𝑙×𝑤×ℎ
2
15. Not an ordinary
cylindrical building
What if you had to
determine it’s volume?
If you had to guess,
where do you think this
is located?
South Africa
16.
17. Model the building as a cylinder
Radius = 30m; Height = 173m
𝑉 = 𝜋𝑟2
ℎ
= 𝜋 30 2 173
= 155,700𝜋
≅ 489,146𝑚3
18. World’s Steepest
Staircase
If you had to guess,
where do you think this
is?
This is part of the Mt.
Huashan Hiking Trail.
Huashan is one of China’s
five sacred mountains and
one of the country’s most
popular tourist
attractions.
http://meant4teachers.com/grade12/math/
foundations-for-college-mathematics
19. Assume the stairs
below reflect the
staircase
10 cm
20 cm
30 cm
DEPTH = 1m
20. 10 cm
20 cm
30 cm
DEPTH = 1m
In order to find
the volume of
these three
stairs, look at
each step as a
rectangular
prism.
21. 10 cm
20 cm
30 cm
DEPTH = 1m
30 cm
20 cm
100 cm
100 cm
20 cm
20 cm
100 cm
20 cm
10 cm
23. A composite figure is a figure that's made up
of several different shapes.
We can just add their volumes to find the
volume of the composite figure.
24. Traditional Textbook Problems
Find a piece of architecture around the
world and make a geometry question from it.
Include a full solution and an image of your
question.
25. We became teachers to help others, why not one
another?
By sharing resources, we share our experience
and expertise, allowing future users of our
resources to keep improving them
28. If you request your name be published next to a
document you submitted, let others know
• Your resource is now being shared amongst
teachers everywhere
Gr. 10 Business Lesson
Plan
(Entrepreneurship)
Submitted by:
Mr. Raymond Barone
