Competency 1
Secondary 3
The Stadium Expansion
Solves a Situational Problem
Task Booklet June 2013
/ The Stadium Expansion Task BookletThe Stadium Expansion
The tennis stadium of the city requires a transformation. The board of directors of the stadium wishes to carry out the addition of an entry to the principal building. The construction of this addition should not involve modifications to the air filtration system of the already existing building.
The council gives you the mandate to determine dimensions of the addition which will respect the established constraints. Here is the information that will enable you to determine the dimensions of the addition.
Information on certain dimensions of the addition
The addition must be as large as possible. It must have the shape of a half-cylinder surmounted by a quarter of a sphere. The board of directors requires that the radius of the addition be 14 metres. The total height of the addition remains to be determined.
General information concerning the air filtration system
The engineers determined the capacity of the filtration system by subtracting from the total volume of the stadium, the volume occupied by the materials and people.
The system must filter the entire volume of air of the building in a maximum of 6 hours.
The system filters 9900 m3/h of air.
Information concerning the stadium
The stadium is composed of a rectangular based prism and a pyramid.
The roof of the stadium, in the shape of a pyramid, has the same base as that of the prism.
The dimensions are given in the diagrams below.
Information concerning the roof of the stadium
Information on the volume occupied by the stands, furniture and other materials
- the stands occupy a volume of 18 462.410 m3.
- the furniture and other materials, i.e. the chair of the referee, benches, the net and its posts, the scoreboard, occupy a total volume of 1.195 m3.
BIM Société GRICSPage 1
/ The Stadium Expansion Task BookletInformation on the number of seats in the stands
For the finals, the city gives 1000 free tickets to young people, whereas it gives 2000 tickets for the semi-finals. The remainder of the tickets available is sold in the same number of days.
The following graph illustrates the number of tickets sold for the finals and semi-finals according to the number of days passed since the beginning of the sales.
Information on the volume occupied by the people present in the stadium
In addition to the spectators, 220 people (employees, security guards, ball boys, ushers, players, etc) are present in the stadium at the time of a match.
Distribution of the people present at the time of a tennismatchCategory / Body Weight (kg) / Percentage of people present in each category
Men / 90.7 / 55 %
Women / 74.8 / 35 %
Children (less than 12 years) / 34 / 10 %
The average volume occupied by a personcan be determined using the function f(x) = 0.0012x.
In this function, xrepresents the mean (average) body weight in kg
andf(x), the average volume occupied per personin m3.
In order to maximize the addition to the stadium, you must take account of the following constraints
Volume of air which the filtration system can filter
- The volume of the stadium
The volume occupied by the stands, furniture and other materials
The volume occupied by the people (spectators and employees)
The total height of the addition is the sum of the height of the half-cylinder and the radium of the quarter of sphere.
Determine the total height of the addition to the stadium.
BIM Société GRICSPage 1