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Baby Bottle Volume Lab
Name:
Period:
You are to determine the volume of the vase pictured here. The photograph on the right shows the
vase and what fills the vase.
Unlike practice problems from textbooks, most real life problems involve "messy" coefficients.
Even if the function is easy to antidifferentiate, the arithmetic is usually tedious.
Objective:
In pairs you will work together to find the volume of the vase and hot tamale using your
calculator to find the equation of the vase and then perform the solid of revolution technique.
Then your group will estimate how many hot tamales are in the bottle err….vase.
In this lab you will learn to...
•
Capture the coordinates of points along the edge of the vase from its photograph
•
Use those points and your calculator to determine a function
•
Set up the definite integral for the volume of the vase (a solid of revolution) using
function
•
Evaluate the integral using your calculator.
Directions
1. You will practice how to come up with the 4th degree polynomial that models a given set of
data.
2. You will calculate the solid of revolution showing all the steps but with the help of your
calculator.
3. Use the picture of the vase and hot tamale
provided to take measurements and transfer that
data to graph paper and to a data chart. (minimum
of 20 data points for the vase and at least 5 for the
hot tamale) Remember to draw your axis through
the middle of each object. Your group should be
using centimeters. Remember the more data
points you choose the more accurate your
regression equation. You want your graph to look
something like this. ===================
4. Take the data and using your calculator find the quartic regression equation for the vase and
use a quadratic and quartic equation for the hot tamale. Graph the equations in your calculator to
make sure the shape makes sense and also to choose whether to use the quadratic or quartic
equation for the hot tamale.
5. Using the equations your group settled on calculate the volume using the solid of revolution
technique.
6. Divide the volume of the vase by the volume of the tamale to estimate how many there were in
the vase. That is the ideal case but since there is some empty space, reduce your answer by a
certain amount. The closest group to the actual answer wins!
7. Write up your findings and using the rubric and put together your lab report. It is strongly
suggested if you want full credit to type everything up (except for graph paper) including the
equations. Use programs such as MATHTYPE or EQUATION EDITIOR.
These directions are for the TI-83. Other calculators may have slight differences.
• Type the data into the calculator's lists
STAT>EDIT
If the lists already have numbers, clear them by placing the cursor on the list name, L1,
press CLEAR, then ENTER.
Type all the x coordinates in L1
Type all the y coordinates in L2
• Find the function that models the data
STAT>CALC>QUARTREG (Do NOT press ENTER yet),
Insert Y1 by VARS>YVARS>Function>Y1
Your home screen should read QuartReg Y1, now press Enter.
If you press Enter too early, clear the screen and try again.
• The screen displays the 4th degree polynomial that models the edge of the vase. This function
is also pasted in Y1. You can graph it. Set your window values so Xmin = 0 and Xmax =
200 and select ZOOM>ZOOMFIT to see your model.
These directions are for the TI-89.
Press [APPS]
Choose 1 FlashApps
Choose Stat/List Editor
If the lists already have numbers, clear them by placing the cursor on the list name, list1, press
[CLEAR], then [ENTER].
• Type all the x coordinates in list1
• Type all the y coordinates in list2
• Press [F4 Calc] to begin doing the regression
• Choose 3 Regression
• Choose 6 QuartReg
• Enter list1 for the X List and list2 for the Y List. For Store RegEqn to: choose y1(x)
This function is also pasted in Y1. You can graph it. Set your window values so Xmin = 0 and
Xmax = 200 and select ZOOM>ZOOMFIT to see your model.
•
•
•
•
Use the regression features of a graphing calculator to find a function that models the given set of
data.
To Practice lets use this set of data.
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 ___________________________ cubic units
Grading Rubric (To ensure you get all the points label each section and subsection clearly.
1. Title page with group name
2. Neatness (try to use MATHTYPE or EQUATION EDITOR) The project should be typed
including the equations.
3. Practice Calculation with
a. Recreated Data Table
b. The regression equation
c. Expression for the volume of the data
d. Work shown for the solving the integral and final answer.
4. Baby Bottle and Hot Tamale
a. Drawn the data points (sketch out the whole shape) and the graph of your regression
equation on graph paper.
b. Data table for Baby Bottle (20 data points min)
Data table for H.Tamale (5 data points min)
c. The regression equation for both
d. Expression to find the volume of each and an expression to find the number of H.
Tamales in the Bottle.
e. Work shown for solving the integral for each.
f. Your final guess once you subtract out the estimate of the empty space.
5. Summary: Answer the following questions
a. What were some areas for potential error?
b. Discuss methods that could have been done to minimize the error. Make sure to tie it
into the Calculus concepts you have learned.
c. What did you learn? Bring a tear to my eye!
d. What if there were more than “3 bumps”? How could you find the volume of a more
wavy container when your calculator is limited to a quartic regression?
e. What did each of the members on the team do? Answers such as “everyone
everything equally” is not sufficient.
f. How can this project be improved?