The document contains summaries of problems and solutions related to geometry concepts in various films. The problems involve calculating volumes of pyramids and rockets, determining speeds and intervals of objects in orbits, finding dimensions of packages, and identifying geometric shapes and concepts like parallelism and symmetry depicted in films.

1. PROBLEMS

2. The Egyptian Pyramids – France 2013
https://www.youtube.com/watch?v=j6PbonHsqW0

3. The Egyptian Pyramids – France 2013
Calculate the volume
of the pyramid whose
base is inscribed in a
circumference with
radius 20 metres…
… and knowing that the
height is equal to the edge
of the base.

4. The Egyptian Pyramids – France 2013
SOLUTION:
First we have to calculate the side of the base:
Using Pitágoras with the triangle COD
Then, the volume of this pyramid is:
So, as we have calculated l, and we
know that h = l

5. 2001: A Space Odyssey – U.K. 1968
https://www.youtube.com/watch?v=GIbX9jXvxNw

6. 2001: A Space Odyssey – U.K. 1968
In the movie monoliths are very important and linked
to the human being development.
Thanks to the book we know that they always follow
the proportion 1: 4 : 9.
• What do these numbers suggest to you?
• What´s the name of their solid?
• Calculate the total surface area of
the monolyth if the measures are
expressed in metres.

7. 2001: A Space Odyssey – U.K. 1968
SOLUTIONS.
What those numbers suggest you?
Are the square of the first whole numbers
• What´s the name of their solid?
Cuboid
• Calculate the total surface area of
the monolyth if the measures are
expressed in meters.

8. Nosferatu – Germany 1922
Angles are very important in
cinema. For example, they are
used by cameramans, directors
of photography or set designers.
Watch the following squence of Nosferatu
movie, and talk about how angles are used in
the scene and for what purpose.
https://www.youtube.com/watch?v=1djGyCj1vCk

9. Nosferatu – Germany 1922
SOLUTION:
The director created a disturbing atmosphere by different ways:
- The scenes are plenty of oblique lines.
- By using deformed proportions.
- Light and shadows change the geometrical shapes.

10. Orbits – Spain 2013
https://vimeo.com/67596206

11. Orbits – Spain 2013
In Orbits, two rockets rotate around the same
planet coinciding at certain intervals.
If we assume that one follows a circular orbit with
a radius of 30, and it takes 12 days a full round…
…and the other one follows an elliptical orbit with
semi-axis 10 and 70, and it goes at the same speed.
How often do the rockets coincide?

12. Orbits – Spain 2013
SOLUTION:
Length of the circunference: 2 x ∏ x r = 60∏
Speed 60∏/ 12 = 5∏/day
Length of the ellipse:
= 100∏
As they go at the same velocity, we can calculate the LCM of the length.
LCM = 300 ∏
That means 300∏ / 5∏ = 60
They coincide every 60 days

13. Out of Bounds – Denmark 2014
https://www.youtube.com/watch?v=cI2Zwr68B-k

14. Out of Bounds – Denmark 2014
How high (x) is the plane flying when that
person falls? We know that the plane took off
15 minutes before, it goes with an average
speed of 300km/h and with an angle of
inclination of 15º.

15. Out of Bounds – Denmark 2014
SOLUTION:
A quarter of hour at 300Km/h = 75 km
Sin15º =
𝑥
75
x = 75·sin15º = 19,41 km

16. Pythagasaurus – U.K. 2011
https://www.youtube.com/watch?v=Q5cab4NMHsY

17. Pythagasaurus – U.K. 2011
Invent your own problem based on this short
movie.
You can link it, for example, to Pythagoras´ or
Thales´theorems, trigonometry…
* Remember that the Pythagasaurus
has a set square shape, so its angles
are 30º, 60º and 90º.

18. Pythagasaurus – U.K. 2011
Invent your own problem based on this short
movie.
SOLUTION: Any solution is valid

19. Mac n´Cheese: Supermarket – The Netherlands 2013
https://www.youtube.com/watch?v=WdJ0LzQv8Ek

20. Mac n´Cheese: Supermarket – The Netherlands 2013
We like this special pyramid formed by cuboid shape
packages.
Calculate the dimensions
of one package knowing
that there is a total of 3
cubic metres of powder.
In each package the lenght is three time the
width a = 3·b and the height is four times h = 4· b

21. Mac n´Cheese: Supermarket – The Netherlands 2013
SOLUTION:
First we need to calculate the number of packages:
19 x 9 + 17 x 8 + 15 x 7 + 13 x 6 + 11 x 5
+ 9 x 4 + 6 x 3 + 4 = 603
Dividing 3 cubic meters by 603=
0,014925 = 14925 cubic centimetres
The volume of this package is a · b · h = 3b · b · 4b = 12b3
Solving 12b3 = 14925 b= 10,75 cm
As a = 3·b = 32,25 cm and h = 4· b = 43 cm

22. Capture the flag – Spain 2015
https://www.youtube.com/watch?v=67YfSzkmDgw

23. Capture the flag – Spain 2015
In Capture the flag the heroes fly to the Moon. They do it in a
rocket which is basically formed by a cylinder, a frustum (trunk of a
cone), and a cone.
There are several kind of cones, which one would have a
higher volume? (Consider all have the same height)
Calculate the volume of the rocket, knowing that it
starts as a cylinder (30m diameter and 50m high),
then the frustum (20 m high), and finally the cone
(15 m diameter and 50 m high)

24. Capture the flag – Spain 2015
SOLUTION:
Itisn´tnecessary to calculatethethreecones, we can decide justseingthe formulas and
comparing
1
12
,
1
6
,
2
15
Withcommondenominatorthey are:
5
60
,
10
60
,
8
60
So theellipticalcone has thehighestvolume.
The volume of therocketistheaddition of thethreesolids:
Volume of cylinder : 𝜋 · 152
· 50 = 35342,917
Volume of frustum:
𝜋·20
12
· 302 + 30 · 15 + 152 = 8246,681
Volume of theellipticalcone:
𝜋·152·50
6
= 5890,486
TOTAL: 35342,917 + 8246,681 + 5890,486 = 49480, 084 cubic metres

25. What is that? – Greece 2007
https://www.youtube.com/watch?v=mNK6h1dfy2o

26. What is that? – Greece 2007
The geometric language is used frequently to
talk about the structure of a screenplay. This
way we can talk about parallel stories, love
triangles, convergence of plots, symmetries,
continuity,…
What geometric word would you use to define
this short movie?

27. What is that? – Greece 2007
SOLUTION:
What geometric word would you use to define this
short movie?
We can accept different words as solution, such as
cycle, periodicity, circumference,…