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```					A project about Pyramids...and Mathematics.
(Source:
http://www.pbs.org/wgbh/nova/pyramid/geometry/index.html )

How Tall?
At 146.5 m (481 ft) high, the
Great Pyramid stood as the
tallest structure in the world
for more than 4,000 years.
Today it stands at 137 m
(449.5 ft) high, having lost
9.5 m (31 ft) from the top.

Here's how the Great
Pyramid compares to some
modern structures.

Draw this pyramid on a piece of paper, according to the
measurements given in the outline following in Task 2.

This outline shows the Great Pyramid's actual dimensions
scaled down using the scale of 1 cm = 30 m.

Scale: 1 cm = 30 m

1. Cut out the pyramid along the solid lines.
2. Fold each triangle side along the dotted lines towards
the centre of the square base.
3. Align the sides of any two triangles and tape into place.
Repeat until the pyramid is complete.

Once you have assembled your scaled-down model of the Great Pyramid, you can
compare it to scaled-down versions of other buildings and objects, including people.
Fill in the missing numbers in the table below:

Scale            Object
Height           to represent
Actual          (1 cm =          scaled-down
Object           Height          30 m)            height
Great Pyramid 146.5 m            4.9 cm         paper pyramid
Statue of Liberty 92 m           ? cm           small paper clip
Sears Building 443 m             ? cm           ball-point pen
Average person 1.7 m             .05 cm (.5 mm) grain of salt
Eiffel Tower      300 m          ?              ?
Leaning
Tower of Pisa 55 m               ?                ?
Big Ben

How Heavy?
More than 2,300,000 limestone and granite
blocks were pushed, pulled, and dragged into
place on the Great Pyramid. The average
weight of a block is about 2.3 metric tons (2.5
tons). How much do all the blocks weigh
together?

Find out how much a Boeing 747 weigh...how
many Boeing 747’s make up the weight of the Great Pyramid?

a. What is the area of one triangle that makes the Great Pyramid? First work it
out in square centimetres. Now times your answer by four to get the total
area of all four triangles in square centimetres.

b. What are the dimensions of the base, height and side edges of the pyramid in
metres? (You need to times the centimetres by 30 to get it into metres.) Now
use your answers to work out the total area of the four triangles in square
metres.

c. What is the total area of the square that makes the base, in square metres?

d. How many Melbourne Cricket grounds (MCG’s) would fit into this base area?

How Deep?
The descending passageway that leads to
the Unfinished Chamber is long, narrow,
steep and, without any windows, very dark!
When you arrive at the burial chamber,
you'll be 20 m (66 ft) beneath the
foundation with over 6 million tons of stone
piled above you!

If the Unfinished Chamber is 20 straight
down from the foundation, and the chamber
sits right in the middle of the Great Pyramid
about 115 metres from the sides, how long is the passage? (This is a tricky
question! You may have to use Pythagoras’ Theorem to solve it...)

Take a virtual tour of this passage way here:
http://www.pbs.org/wgbh/nova/pyramid/explore/khufuenter.html

How Steep?
Each side of the Great Pyramid rises at an
angle of 51.5 degrees to the top. Not only
that, each of the sides are aligned almost
exactly with true north, south, east, and
west.

For a pyramid to look like a pyramid, each
of the four triangular-shaped sides must
slope up and towards each other at the
same angle so that they meet at a point at
the top. The builders constructed the pyramid
layer by layer, starting at the bottom. They had
to check their work often, for even a tiny error at
the bottom could grow into a very large error by
the time the workers reached the top!

If the bottom two angles in a triangle is 51.5
degrees each, how big is the angle at the top of

Perimeter?
The base of the Great Pyramid is a square with each side measuring 230 m (756 ft)
and covering an area of 5.3 hectares (13 acres).

If you were to walk around the base, about how far would you walk?

The most enigmatic of sculptures, the Sphinx was carved from a single block of
limestone left over in the quarry used to build the Pyramids. Scholars believe it was
sculpted about 4,600 years ago by the pharaoh Khafre, whose Pyramid rises directly
behind it and whose face may be that represented on the Sphinx.

The
Sphinx from the rear, gazing
down on Cairo.

Half human, half lion, the Sphinx is 240 feet long and 66 feet high. What are these
dimensions in metres?

We've scaled down the Great Pyramid for you. Now it's up to you to see if you can
create scale models (use a scale of your own choice, but write the scale onto each of
your models) of the other two pyramids on the Giza Plateau, Khafre and Menkaure.
Here are their actual dimensions:

Khafre

   Base: 214.5 m (704 ft) on each side
   Height: 143.5 m (471 ft) tall
   Angle of Incline: 53 degrees 7' 48"

Menkaure

   Base: 110 m (345.5 ft) on each side
   Height: 68.8 m (216 ft) tall
   Angle of Incline: 51.3 degrees

Use Excel to create a timeline of the following information:

Timeline of New Kingdom Pharaohs

Reigned(dates
Dynasty        Pharaoh        in B.C.)

18th Dynasty Ahmose        1570-1546
Amenhotep I 1546-1524
Tuthmosis I 1524-1518
Tuthmosis II 1518-1504
Tuthmosis III 1504-1450
Hatshepsut 1498-1483
Amenhotep II 1450-1419
Tuthmosis IV 1419-1386
Amenhotep III 1386-1349
Amenhotep
1349-1334
IV
(Akhenaten)
Smenkhkare 1334
Tutankhamen 1334-1325
Ay            1325-1321
Horemheb      1321-1293
19th Dynasty Ramses I      1293-1291
Seti I        1291-1278
Ramses II     1278-1212
Merenptah     1212-1202
Amunmesses 1202-1199
Seti II       1199-1193
Siptah        1193-1187
Twosret       1187-1185
20th Dynasty Setnakhte     1185-1182
Ramses III    1182-1151
Ramses IV     1151-1145
Ramses V      1145-1141
Ramses VI     1141-1133
Ramses VII 1133-1126
Ramses VIII 1126
Ramses IX     1126-1108
Ramses X      1108-1098
Ramses XI     1098-1070

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