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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 / 2p

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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