What Limits an Organism S Size? If There Were a Two-Ton Bunny Hopping Down the Street

Abstract gigantic amount of heat form its large digestive process. What limits an organism’s size? If there were a two-ton bunny hopping down the Problem Description street, what would you do? Call the National Guard? Alert the president? We are trying to find the answer to the What would make the rabbit so big? question: How does surface area relate to Why does that question sound so volume ratio? ridiculous? S=Surface Area We are here to answer that question. We L=Side chose this project because the question V=Volume intrigued us. The goal of our project is to A=Area show what limits the size of living Pi=Pi things. R=Radius

Introduction The formula we used to determine the volume of a cube is: V=L3 All living things have basic needs even down to the cell level. Most are very The formula we used to determine the small because nutrients can diffuse in area of a cube is: A=6*S2 and waste can defuse out very easily. If the cells were to get much bigger they The formula we used to determine the would have a hard time getting the volume of a sphere is: V=4PiR3 things they need, such as oxygen, and getting rid of the waste they don’t need, The formula we used to determine the such as carbon dioxide. area of a sphere is: A=4PiR2/3

Most single celled organisms are large Method of Solution enough to let oxygen diffuse in and out easily, larger multi-celled organisms We used an excel spreadsheet to find the need enzymes to break down these area and volume of a cube. This is how compounds and let them into their cells, we did it. which are smaller than those of most single celled organisms. 1. We got the length of a cube (we used 1mm) Large animals such as mammals use 2. We used the area of a cube lungs and organs in the same way most formula which equals A=6*S2. single celled organisms use their cell 3. We used the volume of a cube walls. formula which equals V=6*S3. 4. We determined and compared An animal with a very large surface area the ratio of surface area to would have to metabolize food at a very volume. fast rate because of its high level of heat 5. We determined and compared radiation. The animal would give off a the difference in areas based on the length of a side. 6. We determined and compared 3 27 the difference in volumes based 4 64 on the length of a side. 5 125 7. We graphed our results and 6 216 reached conclusions as to how 7 343 surface area and volume are 8 512 9 729 related. 10 1000 Results 11 1331 12 1728 L SA V Ratio: SA to V 13 2197 1.00 6.00 1.00 6.00 14 2744 1.50 13.50 3.38 4.00 15 3375 2.00 24.00 8.00 3.00 16 4096 2.50 37.50 15.63 2.40 3.00 54.00 27.00 2.00 3.50 73.50 42.88 1.71 Conclusion 4.00 96.00 64.00 1.50 4.50 121.50 91.13 1.33 Based on our results, it is clear that 5.00 150.00 125.00 1.20 Volume increases at a faster rate than 5.50 181.50 166.38 1.09 Surface Area. 6.00 216.00 216.00 1.00 6.50 253.50 274.63 0.92 7.00 294.00 343.00 0.86 If the average dimension of an organism 7.50 337.50 421.88 0.80 cell is doubled, its surface area will 8.00 384.00 512.00 0.75 quadruple, and its volume will increase 8.50 433.50 614.13 0.71 by a factor of 8. If the average linear dimension of the organism is tripled, its area will increase by a factor of 9, and its Difference in Areas volume by a factor of 27. Cube 1 & 2 4 Cube 1 & 3 9 Cube 1 & 4 16 Cube 1 & 5 25 Future Work Cube 1 & 6 36 Cube 1 & 7 49 We would like to continue with this Cube 1 & 8 64 project and determine if there is an Cube 1 & 9 81 optimum ratio for surface area and Cube 1 & 10 100 volume. Cube 1 & 11 121 Cube 1 & 12 144 Cube 1 & 13 169 Cube 1 & 14 196 Cube 1 & 15 225 Cube 1 & 16 256

Difference in Volume Cube 1 Vs. 2 8