Essential Cell Biology (fifth Edition)
Essential Cell Biology (fifth Edition)
5th Edition
ISBN: 9780393680362
Author: ALBERTS, Bruce, Hopkin, Karen, Johnson -
Publisher: W. W. Norton & Company
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Chapter 1, Problem 17Q
Summary Introduction

To calculate: The volume, surface area, and surface-to-volume ratio for a bacterial and animal cell.

Expert Solution
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Explanation of Solution

It is given that,

Diameter of the bacteria cell=1 µm

Diameter of the animal cell=15 µm

Radius=Diameter2

Radiusofthebacterialcell=12×10-6m=0.5×10-6mRadiusofthebacterialcell=152×10-6m=7.5×10-6m

Volumeofasphere=43πr3Surfaceareaofasphere=4πr2

Volumeofasphericalbacterialcell=43π(0.5×10-6)3=43×227×(0.5)3×(10-6)3=0.5237×10-185.24×10-19m3

Surfaceareaofasphericalbacterialcell=4π(0.5×10-6)2=4×227×(0.5)2×(10-6)2=3.14×10-12m2

Volumeofasphericalanimalcell=43π(7.5×10-6)3=43×227×(7.5)3×(10-6)3=1767.656×10-181.77×10-15m3

Surfaceareaofasphericalanimalcell=4π(7.5×10-6)2=4×227×(7.5)2×(10-6)2=7.07×10-10m2

Surfaceareatovolumeratioofanimalcell=7.07×10-10m21.77×10-15m3=3.99×105m-14×105m-1

Surfaceareatovolumeratioofbacterialcell=3.14×10-12m25.24×10-19m3= 0.599×107m-10.6×107m-16×106m-1

Thus, the volume and surface area of the bacteria cell is 5.24×1019m3 and 3.14×1012m2 respectively and of animal cell is 1.77×1015m3 and 7.07×1010m2 respectively.

Summary Introduction

To explain: The change in the ratio of surface area to volume if the internal membranes of the cell are included which is 15 times the area of the plasma membrane in surface area calculation.

Expert Solution
Check Mark

Explanation of Solution

The volume of the animal cell is 3375 times more than bacterial cell, but the surface area increases only 225 times more than bacterial cell. The surface area to volume ratio of the bacterial and animal cell when the surface area is 15 times that of normal changes to

Surfaceareaofbacterialcellincludinginternalmembrane=15×3.14×10-12m2=47.1×10-12m2

Surfaceareatovolumeratioofbacterialcellincludinginternalmembrane=47.1×10-12m25.24×10-19m3=8.98×107m-19×107m-1

Surfaceareaofanimalcellincludinginternalmembrane=15×7.07×10-10m2=106.05×10-10m2

Surfaceareatovolumeratioofanimalcellincludinginternalmembrane =106.05×10-10m21.77×10-15m3=59.91×105m-16×106m-1

The surface area of bacterial and animal cell changes to 9×107m1 and 6×106m1 respectively. Even after including the internal membranes, the surface area to volume ratio remains nearly the same. Thus, the internal membrane of eukaryotic cell helps the cells to grow bigger and yet maintain copious membrane area. Note, bacteria lack membrane-bound organelle and the calculation for bacterial cell is to gain an idea about the change in surface area to volume ration only.

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