The Egg Project

Jessica JooAndy Porter

Purpose

• The purpose of this project is to practice applying the equations we learned in calculus to real-life.

• the project let us see the accuracy of the formulas that we have learned in the class.

• to be familiar with the graphing calculator.

Material List

• Scissors• 2pieces of graph

paper• A ruler• 2 Easter eggs• Measuring cup• Large bowl• Water• Graphing calculator• Utensils• tape

Volume by filling the egg with water

First we prepared the measuring cup and the bowl.

Volume by filling the egg with water

Then we filled in the top and bottom part of the egg with water.

Volume by filing the egg with water

Then we poured the water into the measuring cup.

Volume by filing the egg with water

Water level was at 50 ml!! Because 1 ml = 1 cm3 we concluded that the Volume of the egg is 50 cm3 .

Displacement

First, we taped the egg to make sure the water does not get inside the egg. Then we recorded the water level before we put the egg in the water. Then we carefully placed the egg in the water.

DisplacementBefore After

the water level was at 150ml, after we put the egg in the water, water level raised up to 210ml. To calculate the volume of the egg, 210 ml(after) – 150 ml(before) = 60mlBecause 1 ml=1cm3 , the volume of the egg is 60cm3 .

Surface Area

First, we prepared a scissor and a graph paper. Then we cut out the squares from the graph paper.

Surface Area

We glued the egg surface. Then attached the squares we cut out from the graph paper. The total squares that we used to cover up the egg surface was 396.158(bottom)+238(top)=396A side of a square is 0.5cm. Therefore, to calculate the surface area , 0.5 X0.5X396=99cm2 .

Tables

1 2 3 4 average

Displacement 60ml 55ml 55ml 57ml 56.75ml

Filling the egg with water 50ml 50ml 50ml 50ml 50ml

Top Bottom Total

Squares used 238 158 396

Surface area(cm2) 59.5 39.5 99

VolumeTo be more accurate, we had 4 trials and calculate the average.

Surface AreaA side of a square is 0.5cm. To calculate the surface area, we multiplied number of squares used by 0.5X0.5.

First, we cut the egg in half vertically so that we can sketch the curve of the egg. We placed the egg on the

graph paper and sketched it.

Then we drew the y-axis and x-axis to measure the point. By using a ruler, we found out the distance of

each point from the axis.

Graphical Analysis

Graphical Analysis

We put in the data into the calculator.

By using Quadratic Regression, we got the equation.

2

62 2

0

6 4 3 2

0

5 4 3

[ ( )]

( 0.241558416 1.487812188 .1021978022)

(0.583504807 0.07187188 0.0272376325 0.0304102272 0.0104443908)

0.583504807 0.07187188 0.0272376325 0.030410227[

5 4 3

b

a

V R x dx

x x dx

x x x x dy

x x x

2

60

20.0104443908 ]

2[90.7466758 23.28870489 1.96110954 0.5473840896 0.0626663448]

207.683023 207.6835

xx

By using a disc method, we solved the equation. To reduce the errors, we did not round up the numbers.

Calculation-volume

Calculation- Surface Area2

62

0

2

6 1

2

0

3620

2 ( ) 1 [ '( )]

2 1 [ 0.4831168832 0.1487812188]

1 [0.2334019228 0.1437574374 0.0221358511]

0.4668038456 0.1437574374

2

0.4668038456

2 2[ ]

0.4668038456 3

2

0.466803

b

a

S r x f x dx

x x dx

u x x

du x dx

u du

u

32 62

0

2[ [1 (0.2334019228 0.1437574374 0.0221358511)] ]

8456 313.46001188[14.53004125]

195.5745278

195.575

x x

Analysis

• Calculations of surface area and volume were not close to our estimation. Even though we did not round up any numbers until the last step, the answer was far off from our estimation. Maybe cutting out the graph paper was ineffective way to estimate the surface area.