Group work : Mathematics
by

Winny Van Moeseke
&
Katrien Van Acker

 

 

 

 

 

1. Procedure

First we have chosen a glass out of our collection beer glasses: the Kriek glass.  Afterwards we filled the glass with plaster up to the edge.

After a few days we could start the measurements. We indicated the distances and with a string we measured the circumference of the glass at several heights and calculated the resp. radius. At this point we had enough to make a graph of the contour line of the glass, put in two lists and let the TI-83 find the regression function.


2. Measurements

 

 circumference of the circle = 2rp
r = circumference of the circle / 2
p
 

Height

Circumference

Radius  

o cm

7,8

1,24

1 cm

10,4

1,66

2 cm

13,2

2,10

3 cm

16,4

2,61

4 cm

19,0

3,02

5 cm

20,4

3,25

6 cm

22,3

3,55

7 cm

24,1

3,84

8 cm

25,1

4,00

9 cm

25,6

4,10

10 cm

25,6

4,10

11 cm

25,8

4,12

12 cm

26,1

4,20

      

        

                       

3.   Regression equation

                                  STAT  Calculate  7  L1,L2,Y1

                    

4.   Graph  

 

5.   Questions

  

1.     Find f(x)

        f(x) = 2,489544810.10-4 x4 - 0,0061439051 x3 + 0,0023049071 x2 + 0,4236361188 x + 1,232690692

 

 2.     What is the maximum inner volume of the glass ?

        Maximum inner volume


       

       
 
        = 431,2764081  (in cm3)        (dm3
 l) 
    
   = 431,2764081.10
-3 l
 

 

  

3.     Up to what height must we fill the glass to obtain half of the maximum volume ?

      a) Approximate solution of h' (via table)

 

 

 

 

 

                                                                            

   b) Using SOLVE from CATALOG

   

                               

       Conclusion : If the glass is filled up to 7,92 cm, then the volume of the liquid is half of the maximum inner
       volume

4.     How many glasses, filled up to 90%, can we pour out of a Magnum bottle (1,5 l)?

 

      9/10 . 431,2764081.10-3 l = 388,1487673.10-3 l

      1,5 : 0,3881487673 = 3,8644977
 

      Conclusion :out of a Magnum bottle of 1,5 l, almost 4 Kriek glasses can be filled up to 90%.

 

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