Chapter 2, Problem 73TQ

Summary Introduction

To review:

The derived values of surface area to volume ratio that indicate the evolutionary changes to form the eukaryotes.

Introduction:

A prokaryotic cell is a single-celled organism that is devoid of a well-defined nucleus. They are microscopic in size and lack membrane-bound cell organelles. Eukaryotic cells are multicellular organisms that have a well-defined nucleus and membrane-bound cell organelles. They are different from prokaryotes in terms of size and complexity.

The length of Escherichia coli (E. coli) is 2 micrometer (µm), the diameter is 1 µm, and the radius is 0.5 µm. The diameter of a eukaryotic cell is 20 µm and the radius is 10 µm.

The surface area of a cylinder is given by

${\text{A=2πr}}^{\text{2}}\text{+2πrh}$

The volume of a cylinder is given by

${\text{V=πr}}^{\text{2}}\text{h}$ .

The surface area of a sphere is

${\text{A=4πr}}^{\text{2}}$

The volume of a sphere is given as

$\text{V=}\frac{{\text{4(πr}}^{\text{3}}\text{)}}{\text{3}}$ .