Three cubes with sides of 1 cm, 2 cm and 3 cm each and a table with surface area, volume, and ratio of surface area to volume calculated for each cube.

FIGURE 10–1 Ratio of Surface Area to Volume As the length of the sides increases, the volume increases more than the surface area. Interpret Tables What are the ratios comparing?

ddd

A partially folded cut out pattern for a cube.

▸ Ratio of Surface Area to Volume Imagine a cell that is shaped like a cube, like those shown in Figure 10–1. The formula for area (l × w) is used to calculate the surface area. The formula for volume (l × w × h) is used to calculate the amount of space inside. By using a ratio of surface area to volume, you can see how the size of the cell's surface area grows compared to its volume.

Notice that for a cell with sides that measure 1 cm in length, the ratio of surface area to volume is 6/1 or 6 : 1. Increase the length of the cell's sides to 2 cm, and the ratio becomes 24/8 or 3 : 1. What if the length triples? The ratio of surface area to volume becomes 54/27 or 2 : 1. Notice that the surface area is not increasing as fast as the volume increases. For a growing cell, a decrease in the relative amount of cell membrane available creates serious problems.

Quick Lab
OPEN-ENDED INQUIRY

Modeling the Relationship Between Surface Area and Volume

  1. Use the drawing and grid paper to make patterns for a 6-cm cube, a 5-cm cube, a 4-cm cube, and a 3-cm cube.

  1. Cut out your patterns and fold them. Then use the tabs to tape or glue the sides together. Don't tape down the top side.

  1. Construct a data table to compare the volume, the surface area, and the ratio of surface area to volume of each cube.

  1. Use your data to calculate the number of 3-cm cubes that would fit in the same volume as the 6-cm cube. Also calculate the total surface area for the smaller cubes.

    Analyze and Conclude

  1. Review Describe the function of a cell membrane and its relationship to what happens inside a cell.

  2. Apply Concepts How does the surface area change when a large cell divides into smaller cells that have the same total volume?

End ofPage 275

Table of Contents

Miller & Levine Biology
About the Authors
Changing the World of Biology Education
Contents
Diversity of Life: A Visual Guide DOL•1–DOL•64
Labs and Activities
Features
UNIT 1 The Nature of Life
1 The Science of Biology
2 The Chemistry of Life
Unit Project
UNIT 2 Ecology
3 The Biosphere
4 Ecosystems and Communities
5 Populations
6 Humans in the Biosphere
Unit Project
UNIT 3 Cells
7 Cell Structure and Function
8 Photosynthesis
9 Cellular Respiration and Fermentation
10 Cell Growth and Division
Unit Project
UNIT 4 Genetics
11 Introduction to Genetics
12 DNA
13 RNA and Protein Synthesis
14 Human Heredity
15 Genetic Engineering
Unit Project
UNIT 5 Evolution
16 Darwin's Theory of Evolution
17 Evolution of Populations
18 Classification
19 History of Life
Unit Project
UNIT 6 From Microorganisms to Plants
20 Viruses and Prokaryotes
21 Protists and Fungi
22 Introduction to Plants
23 Plant Structure and Function
24 Plant Reproduction and Response
Unit Project
UNIT 7 Animals
25 Introduction to Animals
26 Animal Evolution and Diversity
27 Animal Systems I
28 Animal Systems II
29 Animal Behavior
Unit Project
UNIT 8 The Human Body
30 Digestive and Excretory Systems
31 Nervous System
32 Skeletal, Muscular, and Integumentary Systems
33 Circulatory and Respiratory Systems
34 Endocrine and Reproductive Systems
35 Immune System and Disease
Unit Project
A Visual Guide to The Diversity of Life
HOW TO USE THIS GUIDE
THE TREE OF LIFE
Bacteria
Protists
Fungi
Plants
Animals
Appendices
Appendix A Science Skills
Appendix B Lab Skills
Appendix C Technology & Design
Appendix D Math Skills
Appendix E Periodic Table
Glossary
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q, R
S
T
U
V
W
X, Y, Z
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Credits
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