Becker's World of the Cell 9th Edition by Lewis Kleinsmith, Jeff Hardin, Gregory Paul Bertoni

Exercise 3

Sizing Things Up. To appreciate the sizes of the subcellular structures shown in Figure 1A-2, consider the following calculations:
(a)All cells and many subcellular structures are surrounded by a membrane. Assuming a typical membrane to be about 8 nm wide, how many such membranes would have to be aligned side by side before the structure could be seen with the light microscope How many with the electron microscope
(b)Ribosomes are the cell structures in which the process of protein synthesis takes place. A human ribosome is a roughly spherical structure with a diameter of about 30 nm. How many ribosomes would fit in the internal volume of the human liver cell described in Problem if the entire volume of the cell were filled with ribosomes
(c)The genetic material of the Escherichia coli cell described in Problem 1-2 consists of a DNA molecule with a diameter of 2 nm and a total length of 1.36 mm. (The molecule is actually circular, with a circumference of 1.36 mm.)To be accommodated in a cell that is only a few micrometers long, this large DNA molecule is tightly coiled and folded into a nucleoid that occupies a small proportion of the cell's internal volume. Calculate the smallest possible volume the DNA molecule could fit into, and express it as a percentage of the internal volume of the bacterial cell that you calculated in Problem.
Problem
Cell Sizes. To appreciate the differences in cell size illustrated in Figure 1A-1, consider these specific examples. Escherichia coli, a typical bacterial cell, is cylindrical in shape, with a diameter of about 1 µ m and a length of about 2 µ m. As a typical animal cell, consider a human liver cell, which is roughly spherical and has a diameter of about 20 µ m. For a typical plant cell, consider the columnar palisade cells located just beneath the upper surface of many plant leaves. These cells are cylindrical, with a diameter of about 20 µ m and a length of about 35 µ m.
(a)Calculate the approximate volume of each of these three cell types in cubic micrometers. (Recall that V = r 2 h for a cylinder and that V= 4 r 3 /3 for a sphere.)
(b)Approximately how many bacterial cells would fit in the internal volume of a human liver cell
(c)Approximately how many liver cells would fit inside a palisade cell