The Egg Project

Max, Nick, Riley

Purpose

• Shows us how to apply calculus with everyday materials

• Shows us how to apply calculus to possible scenarios

• Shows that calculus can be used to solve many questions

Materials and Resource List( All found in the men’s bathroom!! )

• 600 mL Beaker • 150 mL Beaker• 100 mL Graduated Cylinder (that’s right, its already graduated)• H2O (Water for you non science kids *cough* “Mari” *cough*)• Plastic Egg with a smiley face (Must have been on drugs)• TI-89 Titanium (Kmet’s better half)• TI-84+ (borrowed)• Caliper (the precise instrument for egg calculation)• Ruler (also borrowed)• Pencil • Paper (taken from recycle bin)• Graph Paper • Quarter Inch Masking Tape (fell from the sky)• Kmet’s Brain (in other words, the TI-89 Titanium)• Riley’s Brain (not so much)• Max’s Taping Ability and Caliper skills (because he is too lazy to do math)• Gibbon’s: Computer, keyboard, desk, mouse, rolling chairs, stool, hand

sanitizer, kleenex, stapler (which Riley broke & then fixed), hole punch (when we got bored), hall pass (used as an excuse for Max’s frequent ‘bathroom’ visits)

Method for Surface Area

• Wrap an egg with tape

• Calculate the area of each strip of tape after peeling off

• Add area for total surface area =80.665cm2

Data

Volume Method

Test 1 Test 2 Test 3 Avg. Volume

Water in Egg 58mL 55mL 60mL 57.667mL

Displacement 70mL 60mL 65mL 65.000mL

Width (cm) Length (cm) Width (cm)

Length (cm)

.62 1.81 .62 14.10

.62 2.10 .62 13.38

.62 1.36 .62 12.11

.62 7.68 .62 2.52

.62 10.04 .62 3.57

.62 11.87 .62 2.89

.62 13.21 .62 3.46

.62 13.83 .62 3.60

.62 14.34 .40 2.03

.43 1.70 Total Area

80.665 cm2

Volume:

Area:

Volumetric Average of Both Methods = 61.334mL

Graphical AnalysisX (cm) Y (cm)

0 0

.66 1.185

1.28 1.653

1.916 1.987

2.572 2.184

3.198 2.291

3.84 2.291

4.475 2.225

5.104 2.012

5.737 1.540

6.42 0

Y

X

105695.42707.1216012. 2 xxY220825.14468.1100893.01195. 23 xxxY

003095.31815.201523.1215973.017751. 234 xxxxY

Our Regressions

(calculated with the TI-89 Titanium)

Volume: (Disc Method)

42.6

0

22 )105695.42707.1216012.( dxxxV

dxxRVb

a 2)]([

358268 cm.

42.6

0

223 )220825.14468.1100893.01195.( dxxxxV

223442.6

0

)003095.31815.201523.1215973.017751.( xxxxV

3720.68 cm

3427.69 cm

3910.68 cmAverage Volume:

Surface Area

b

a

dxxfxrS 2)]([1)(2

42.6

0

22 )42707.1432024.(1)105695.42707.1216012.(2 dxxxxS

42.6

0

2223 )14468.1201786.03585.(1)220825.14468.1100893.01195.(2 dxxxxxS

42.6

0

23234 )31815.203046.2647919.071004.(1)003095.31815.201523.1215973.017751.(2 dxxxxxxxxS

2681.81 cm

2077.80 cm

2334.83 cm

2697.81 cmAverage Surface Area:

Comparative Analysis

Volume:

• Calculated Average: 68.910 mL

• Measured Average: 61.334 mL

• Difference: 7.576 mL

Surface Area:

• Calculated Average: 81.697 cm2

• Measured Area: 80.665 cm2

• Difference: 1.032 cm2

The calculated average may be an overestimate because the regression lines were slight overestimates. The measured averages may likewise be underestimates because of difficulties with the water and filling the egg.

The calculated average may be an overestimate because the regression lines were slight overestimates. The measured area might be a slight underestimate due to gaps between the tape when measuring.

The End