To check your work, a sample solution is provided.

We used the following data points

X

Y

X

Y

X

Y

X

Y

0

40

54

46

112

19

163

18

7

40

70

39

121

16

172

19

16

44

80

34

133

15

183

24

26

48

89

30

145

15

200

34

36

48

100

23

155

16

Using the TI-83/TI-89, our quartic regression equation (rounded to 4 decimal places) was

The volume of the vase was determined by:

The computed value for this was 664686.246094 cubic pixels

Using the ratio of  1 cm = 4 pixels (Vase height of 50 cm = 200 pixels), this converts to

Your volume should be approximately between 10,000 and 11,000 cubic centimeters.