Power point problemas with solutions

PROBLEMS

The Egyptian Pyramids – France 2013

https://www.youtube.com/watch?v=j6PbonHsqW0

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.

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

2001: A Space Odyssey – U.K. 1968

https://www.youtube.com/watch?v=GIbX9jXvxNw

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.

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.

Nosferatu – Germany 1922Angles 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

Nosferatu – Germany 1922SOLUTION: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.

Orbits – Spain 2013

https://vimeo.com/67596206

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?

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

Out of Bounds – Denmark 2014

https://www.youtube.com/watch?v=cI2Zwr68B-k

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.

Out of Bounds – Denmark 2014SOLUTION:A quarter of hour at 300Km/h = 75 km

Sin15º = x = 75·sin15º = 19,41 km

Pythagasaurus – U.K. 2011

https://www.youtube.com/watch?v=Q5cab4NMHsY

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.

Pythagasaurus – U.K. 2011

Invent your own problem based on this short movie.

SOLUTION: Any solution is valid

Mac n´Cheese: Supermarket – The Netherlands 2013

https://www.youtube.com/watch?v=WdJ0LzQv8Ek

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

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 centimetresThe 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

Capture the flag – Spain 2015

https://www.youtube.com/watch?v=67YfSzkmDgw

Capture the flag – Spain 2015In 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)

Capture the flag – Spain 2015SOLUTION:Itisn´tnecessary to calculatethethreecones, we can decide justseingthe formulas and comparingWithcommondenominatorthey are: So theellipticalcone has thehighestvolume.

The volume of therocketistheaddition of thethreesolids:Volume of cylinder : Volume of frustum: Volume of theellipticalcone: TOTAL: 35342,917 + 8246,681 + 5890,486 = 49480, 084 cubic metres

What is that? – Greece 2007

https://www.youtube.com/watch?v=mNK6h1dfy2o

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?

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,…