INTRODUCTION - fill the blank for full credit
bank: 3 boys, divide, surface, compare, girl, volume
 You will build cubes of different dimensions.  The dimension along one side will be doubled with each model. You will then calculate the surface area, volume, and the ratio between the two. A ratio is used to _______________
2 quantities. To find the ratio you ________ one quantity by the other. If a ratio girls/boys is 3:1, it means there
are ________________ for every ____________. Find the ratio girls/students in this class ______________
Find the ratio boys/students in this class ___________. If you compute the ratio surface/volume of a cube, you will find out how much ___________ (cm²)  is available  for every unit of _________ (that is 1cm³).

PROCEDURE
Remember: Volume ( cm³)  = V = L (cm) x W (cm) x H (cm)    (for a cube or any box)
total surface  area (cm²)=  A = sum of the areas of the faces = L (cm) x W(cm)  x 6

step1: Measure one size of one cube. 1 side = _____ cm. So volume of 1 cube = ______ cm³ (see above).
Surface = _____ cm² (see above). The ratio surface / volume = A / V = _________. (just divide )
Look at the TABLE BELOW. I reported step1  measurements in the table.

step2: Now build a cube with a side = 2cm. Find its total area A , its volume V and the ratio A/V.
Fill the table below. (see step 1).

step3: do the same thing again for a cube with side = 3cm and then with a cube with side = 4cm. Fill the table.

DATA TABLE: Cell size comparison
cell:	dimension (cm)	Surface area A (cm2)	volume V (cm3)	ratio : Surface area to volume
1	1 x 1 x 1	(1 x 1) x 6 = 6	1 x 1 x 1 = 1	6/1 = 6
2	2 x 2 x 2	_______________	__________	_____________
3	___________	_______________	____________	____________
4	_________	_______________	____________	___________

ANALYSIS

1)
Which model has the largest surface area? ______

Which model has the largest volume? ______

Which model has the largest ratio? ______

So,  as you increase the volume of the cube or any object, the ratio surface/volume ___________. This means there is less surface available per each unit of volume.  

2)
A mouse needs to eat all the time to stay alive, whereas large animal like elephant need to eat only once in a while to keep their metabolism going . Can you understand why after doing this lab ? (a model for a mouse would a a small cube and a model for an elephant would be a big elephant).


3) Is it better to peel off 1 pound of small potatoes or 1 pound of large potatoes ? why ?

4) Every living thing processes food for energy. This energy creates heat that radiates from its surface.
A) why do large object cool more slowly than similar small object ?

B) why is a beached whale more likely than a beached dolphin to experience overheating ?

C) Why are larger mammals found closer to the poles than the equator ?

D) If a woman and a small child fall in a cold lake, why is the child in greater danger of hypothermia ?

E) why elephant have large ears?

GOING FURTHER (try without hints)

In Sciences (Physics, bio or Chem) finding the ratio between 2 quantities is an  important tool. It allows you to investigate the relationship between 2 quantities and to compare them. Here some simple problems involving ratios:

1) The movie Austin Powers features Dr. Evil and his clone Mini Me. Mini Me is much smaller even if identical to Dr. Evil. Mini Me (in the movie) is said to me 1/8 of Dr Devil's size. Let's find out if this makes sense.
 If Mini Me is 32 inches and 1/8 of Dr. Evil, how tall is Dr. Evil (in inches) ? Does this make sense ?
hint: the scale (ratio)  is 1 inch (Mini ME) to 8 inches (Dr. evil). 1 foot = 12inches


2) In 2004, the population density (number of people per unit area) of the united states reached 80 people per square mile. How many people would you expect around Lake Wobegon, Minnesota, an area of 50 square miles?


3) One of the MOST densely populated cities in Macau (a Chinese territory under Portuguese administration) with about 446,250 inhabitants living on 21 square kilometers of land. What is the population density per square kilometer in Macau ? (that is the number of people per square kilometers) (hint: divide people by area)


4) According to Plato's description, the population of the lost city of Atlantis was between 6 and 10 millions people. If  the area of Atlantis was 86,400 square kilometers and he population is assumed to have been 8,640,000 inhabitants, what was the population density for Atlantis (in people/km²) ?


5) Another densely population city is Monaco with 31,980 inhabitants living on 1.95 square kilometers of land. What is the population density per square kilometer in Monaco ?


6) A student is paid at the rate of $38 for 8 hours of work. What is the rate per hour?

7) Which is the fastest-growing plant you know ? A bamboo grew 36 inches in a 24 hour period. What was the hourly growth rate for this plant (in inches per hour that is in/hr)
That means: In every hour, the plant grows ____________, in 3 hours it grows ___________

8) The fruit with the lowest caloric value is the cucumber. A 1 1/2 pound cucumber as 109.5 calories. What is the caloric rate per pound of cucumbers ? (that is calories per pound cal/lbs, remember: 1 1/2 = 1.5)


9) A burger king hamburger has 275 calories and weighs 110 grams. Find the number of calories per gram.


10) THe fruit with the highest caloric value is the avocado: 1 1/2 pounds of edible avocado contain 1110 calories. What is the caloric rate per edible pound ?

11) The air distance between New york and DAllas is 1375 miles. If a plane takes 21/2 hours to make the flight, what is the planet's rate of travel (that is miles traveled per hour that is the speed) ?


12) One of the fastest marathon runners is Balaine Desimo, who completed 26 miles in 2.1 hours. TO the nearest mile, what was his rate of travel ?(his speed = miles per hour)

13) elephants eat more than 1400 pounds of food a week How many pounds of food per day is that ? (pounds per day)

14) An AMerican alligator lives about 40 years and, during that time, grows about 3000 teeth, How many teeth per year is that ?

15) A Llama can travel 60 miles in three days. How many miles per day ?

16) you take a Microsoft Windows Professional class. It costs $698 for 21 hours. Find the cost per hour ?

17) A rhinoceros beetle weighs 30 grams and can carry 850 times its body weight, that is 25,500 grams. If a person could carry proportionally as much as the rhinoceros beetle, how much could a 60 kg student carry.

(answer in pounds: 100,000 pounds)


18) A leaf-cutting ant weighting 1.5 grams can carry a leaf weighting 4.5 grams. If a person could proportionally carry as much weight, how much could a 60kg student carry?