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Homework answers / question archive / Scene #1) The Rock of Gibraltar – Mediterranean sea On a yacht traveling into the Mediterranean Sea, 3D XYZ illegally netted 1000 stingrays
Scene #1) The Rock of Gibraltar – Mediterranean sea
On a yacht traveling into the Mediterranean Sea, 3D XYZ illegally netted 1000 stingrays.
Investigators are not sure how these stingrays will play into the World Conquering Device.
I’m ready to ransack countries along my #1 sea! Unless you can do math in 3D you won’t catch me! On my trip, I bought a model of my favorite rock, The Rock of Gibraltar, but is it to scale?
The Real Deal
426m
6.5 km
800 m
The Scale Model
8.52 cm
130 cm
16 cm
Are these figures similar, congruent or neither?
CONGRUENT Þ 11
SIMILAR Þ 96
NEITHER Þ -37
Scene #2) Pyramids - - Saqqara, Egypt
3D XYZ is suspected to have raided two different pyramids and left with baskets full of Egyptian jewels and a dozen mummies?
Pharaoh Sahure wanted to show Pharaoh Userkaf that he was more awesome, so he made up a game…
My pyramid can hold more stuff than your pyramid
Did pharaoh sahure succeed? Find the difference between the volumes of the pyramids. (Round to the nearest meter)
(Sahure – Userkaf) = D
Sahure 78.75 m
78.75 m
47 m
Userkaf
73.3 m
73.3 m
49 m
D = ______
Scene #3) Parthenon - - Athens, Greece
Etched into the ancient grounds of the Acropolis, 3D XYZ left this note. Investigators suspect 3D XYZ stole stone columns from the Parthenon.
When I get home I’m building my own Mini-Parthenon out of concrete! How much will I need?
A = QTY: 1
B = QTY: 6
C = QTY: 1
D = QTY: 2
|
QTY |
PART |
DIMENSIONS |
TOTAL VOLUME |
|
|
A |
Height = 12 feet; Triangle Length = 36 feet Prism Width = 10 feet |
|
|
|
B |
Height = 20 feet Diameter = 2 feet |
|
|
|
C |
Length 36 feet Width = 10 feet Height = 4 feet |
|
|
|
D |
Length 28 feet Width = 8 feet Height = 2 feet |
|
What is the total amount of concrete needed to the nearest cubic foot?
O = ____
Scene #4) National Roman Museum - - Rome, Italy
After breaking into the Roman Museum, 3D XYZ escaped with a classic trebuchet and a truck load of stone boulders.
Let’s pack some spheres! It’s estimated that when packing spheres only 63% of the total possible volume can be used.
(This is just an example. If a closet was 100 ft3 and each sphere was 1 ft3 this would mean ideally 100 spheres could fit. But with irregular packing it would be 63% of 100 or 63 spheres)
At my apartment I have a closet with 250 ft3 worth of space. If each of my spherical cannonballs have a radius of .75 feet, how many can I fit in my closet? Choose the best approximation from the choices below for your next clue.
89 CANNONBALLS = 89
141 CANNONBALLS = 141
168 CANNONBALLS = 168
Scene #5) Le Paradis Palace - - Tunis, Tunisia
In the largest art museum in Tunisia, 3D XYZ is suspected to have stolen all of the renowned octagonal hanging lanterns.
I stole all the awesome octagonal Tunisian lanterns! They do have this one lantern left. Figure out which shape it will make if it is folded together AND its surface area.
9 cm 13 cm 32 cm
Pentagonal Pyramid
Pentagonal Prism
Hexagonal Prism
Hexagonal Pyramid
This symbol will be equal to the total surface area of the lantern to the nearest cm2.
Scene #6) Matoyianni Street - - Mykonos, Greece
A Greek bakery was surprised to find their wedding cake inventory was robbed. Investigators suspect 3D XYZ just wanted to eat some cake. Later they were sent a cryptic text.
The Mediterranean folks know how to bake. They specialized in scrumptious layered cakes.
How many square inches of icing will be needed to turn an ordinary pile of chocolate into a mouth-watering desert? Use the two diagrams on the left to figure it out. (Hint: you will not put icing on the areas covered by the other layers)
3 in 3in 3in
Choose the best estimate for the square inches of icing needed.
359 in2 Þ X = 359
362 in2 Þ ◊ = 362
367 in2 Þ ? = 367
From above 5 in 5 in 6 in
14 in 8 in
14 in 8 in
You shoulda gave up when math was just in 2D!
D - O - D - 5? - 5X - 5◊
