egg project pgu unna
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mathsTRANSCRIPT
Egg project
PGU Unna
Project ideas - brainstorming
Volume of an eggMethod 1:Experiment of Archimedes
First, you have to fill a beaker with water and note
the level. Then, you put the egg inside and
compare the level to the one without the egg. The
difference is the egg‘s volume. Eureka!
V=π*r²*h
We got:
V=28,09 cm³
Volume of an egg
• Method 2: approximation by a
sphere:
³08,25
2,24
3 3
cmV
cmrrV
Volume of an eggMethod 3:Experiment with egg slices
First, cut your egg into
slices, then calculate the
volume with this
formula.
V= π*r²*h
Our solution is 36.84
cm³
Volume of an egg
• Method 4: by using a formula
³21,34
32,24
34
3
2
2
cmV
V
baV
b=h/2
h
a
We compare: volume of an egg
Method1: 28,09 cm³
Method 2: 25,08 cm³
Method 3: 36,08 cm³
Method 4: 34,21 cm³
We have to say that could not use the
same eggs, but we tried to use some
of similar size.
We compare: volume of an egg
There are a lot of ways to approximate
the volume. The easiest would be the
Archimedes‘ experiment, the most
laborious is the experiment with egg
slices
To conclude: You can find the most
difficult formulas, but at last, you‘ll end
up rounding your results anyway.
Offical egg sizes
• Small eggs: mean 51 g (<53g)
• Medium eggs: mean 59,43g (53g -
62,9g)
• Large eggs mean: 65,45g (63g-
72,9g)
• Extra large eggs: Ø 73,99g (73g)
What about the percentage of a L-egg in
comparision to a M-egg? It is about 10%
more.
Specific weight of an XL-egg
G = 54,7g
V = 50,6cm³ (via formula)r = = 1,081specific weight/ density of our egg
Specific weight Ø 1, 08
Geometry of an egg
Construction with circle and compass.
It is an egg tangram.
Tangram pics of an egg
Work for the international team Spain by Henrike Rabe
Geometry of an egg
Construction with GeoGebra
Geometry of an egg
With a specific tool, GeoGebra constucts an egg
only by determinating points a and b.
Egg Art
Egg Art
Egg Art
Egg Art
Egg Art
Easter eggs from Lindt company
The weight of Lindor eggs
1. We weighted the eggs from the Lindor company
2. We compared it to the reported weight
3. Wait… The weighted mass isn’t the same as the reported one!
With 6,2 g this egg is one of the biggest! But …
Easter eggs of Lindt company
So most of the egg will be between 4,78 g and 5,11 g.
We thought of testing more packages and eggs. Would we get some testing eggs from the Lindt company?
Our letter to the Lindt company
Reply from the Lindt company
Sold out!
The Lindt company could not send us
some more Lindor packages for
testing, no more easter eggs, all sold
out, ….
That‘s why it was after eastern and so
we bought the four last packages in a
super-market in Unna but nevertheless
…
… an early end of our statistics with Lindt eggs
Unfortunately, we were‘t able to work
more with the Lindt eggs, because
they somehow disappeared - maybe it
was a mouse …
Math tasks about eggs
1. A record egg
The biggest egg was laid by the `elephant-bird
´on Madagaskar. One egg has a volume of 9l.
This is like 150 chicken eggs or like 8 eggs
from an ostrich.
Which volume does a chicken and ostrich egg
have?
Math tasks about eggs2. Kiwi egg
The biggest eggs in comparison to their height
the Kiwi from New Zealand. One egg usually
weights of the Kiwis weight.
One Kiwi weights about 1,5 to 2kg
How much weights one egg?
Big Kiwi-eggs weight up to 450g .
How much does the Kiwi weight?
Math tasks about eggs
3. Eggs with surprise
The jeweller Carl Farbergé has built some gold
eggs for his tsar. In every egg was a little
surprise.
For example a copy from the tsar-coach.
The coach was 9,3 cm long and it was built in
the scale 1:75.
How big was its original ?
Sources
Specific weight – information about the average s.w. :
http://www.zeno.org/Meyers-1905/A/Ei
Geometry of an egg – picture: http://www.dynamatadmin.oriw.eu/upload_pdf/20121022_154322__
6.pdf
Das Ei-Projekt, Klett, Mathe Live
http://
www.klett.de/sixcms/media.php/185/allerlei_rechnerei.pdf