Final Culminating Assignment
The International Olympic Committee (IOC) for the 2016 summer games in Rio, Brazil has hired you to
administer the medals. It is your job to come up with the final cost of making the medals based on the
information that the IOC has provided you.
Part A – Measurements/Shape
The gold medal will be a square based rectangular prism with a square based pyramid on top of the
rectangular prism. The height of the rectangular prism is 15 cm. The angle of depression from the top of
the square based pyramid is 38° and the interior height of the square based pyramid is 5 cm. Because
the cost of gold is really expensive, the shape of this medal will be dipped in gold and it is up to you
mathematically decipher the surface area of the shape that is needed to be coated.
The silver medal is a truncated right cone (truncated means the bottom portion of a right cone). The
height of the truncated medal is 3 cm, the radius on the bottom of the medal is 2.2 cm and the radius on
the top of the medal is 1.5 cm. The height of the cone used to design the truncated medal is 5.2 cm. You
are to make the entire medal out of silver, and as such need to figure out the volume of the medal.
The bronze medal is a bronze cylinder with a bronze sphere attached to the top of the cylinder. The
height of the cylinder is 4.2 cm and has a radius of 2 cm, whereas the sphere has a radius of 2 cm as well.
The entire medal will be made of 100% bronze material. You are to determine the total volume of both
the cylinder and the sphere.
Part B – Cost of each medal
Gold Medal
The following graph represents the cost of the gold medal. You are to create a linear equation of this
situation and determine the cost of one medal.
Cost of Gold
400
300, 375
350
Cost ($)
300
250
200, 250
200
150
100, 125
100
50
0
0
50
100
150
200
Surface Area (cm squared)
250
300
350
Silver Medal
The density of silver is 10.5g/cm3 (10.5g/ml).
The equation for density is – d =
mass
volume
The cost of silver is proportional to the following linear equation –
2
C ( m) = m where C = Cost and m = mass in grams
9
You need to create a graph for this linear equation and indicate the cost of one silver medal.
Bronze Medal
The volume of bronze has a relationship to the mass in grams, 5cm3 to 40g. Graph the volume as a
function of mass and derive the equation of this graph in order to identify the mass of bronze required to
make one medal.
Finally, bronze costs $1.94/ounce; determine the cost of one bronze medal.
Part C – Number of Gold Medals
*Note that once you found out how many gold medals are needed for these Olympics, you can deduce that
the same amount will be needed for silver medals and bronze medals.
You will need to simplify add together each section of medals (indoor medals, outdoor medals, track
medals, and team medals). Then solve for ‘x’ to identify how many medals are needed for each section.
1) Indoor Medals
é
( 24x ) ·2 3x - êë
2) Outdoor Medals
( x ) · ( 4x)
( 2x ) ·3· ( x )
2
3
3 2
2
3) Track Medals
4) Team Medals
Total Medals
(
3
ù
4· 3 ú
û
)
2 2
2
2 2
4(x +10)
43
2x 2 +13x + 20
*ONCE YOU ARE DONE, SEE MR. WILLARD TO VERIFY THAT YOU HAVE THE CORRECT ANSWER*
Part D – Labour Costs to make medals
Two reputable companies submitted contracts to you to make the gold, silver and bronze medals.
Company A charged $28 for every medal made with an initial charge of $100. Company B charges $50 for
every 2 medals made with an initial charge of $850. Who would be the better company to hire and why?
At what point would it be better to use the other company and why? Finally, state the range and domain
of both companies where their costs would be better than the other companies cost. This is needed in
case the IOC needs to change the amount of medals required between now and 2016.
Part E – Athletes loosing their medals
Finally, the IOC has noticed that athletes have lost their medals or had them stolen and they want to have
an idea of how many medals are lost or stolen between men and women. The IOC knows is that 850
medals were handed out in the last Summer Olympics. They also know that 142 medals were replaced;
they also noticed that 20 % of male athletes had their medal lost or stolen, whereas 12% of female
athletes had their medals lost or stolen. Calculate how many medals needed to be returned to men and to
women.
Answer Sheet
Part A – Measurements/Shape
Surface Area of Gold
_____________________________
Volume of Silver
_____________________________
Volume of Bronze
_____________________________
Part B – Cost of Medal
Cost of Gold
____________________________
Cost of Silver
____________________________
Cost of Bronze
____________________________
Part C – Number of Gold Medals
1) Indoor Medals
___________________________
2) Outdoor Medals
___________________________
3) Track Medals
__________________________
4) Team Medals
__________________________
Part D – Labour Cost
Who would be the better company to hire and why?
At what point would it be better to use the other company and why?
Range and domain of both companies
Part E – Athletes losing medals
How many medals did the males lose?
__________________________
How many medals did the females lose?
__________________________