Chapter 9, Problem 17STP

Summary Introduction

To infer:

How the ratio of surface area to volume changes as a cell grows larger

Introduction:

A cell grows until it reaches its size limit, then it either stops growing or divides. Most cells undergo division. Cell division helps a cell to reproduce and makes the organism grow and heal certain injuries. Most cells are less than 100μm in diameter. The ratio of surface area to volume is the key factor that limits the size of a cell. By remaining small cells have a higher ratio of surface area to volume and they can sustain themselves more easily.

Answer to Problem 17STP

Asthe cell grows larger the ratio of surface area to volume decreases. This will continue to decrease if the cell grows in size. The volume increases more rapidly than the surface area and so the cell has difficulty in transporting nutrients and waste products.

Explanation of Solution

Surface area of a cell refers to the area covered by the plasma membrane through which the nutrients and wastes must pass through. Volume refers to the space taken up by the contents of the cell. To calculate the surface area of the cube, we have to multiply length times width times the number of sides. To calculate the volume, we have to multiply length times width times height.

Suppose the length of a cell is 1cm.

  ${\text{Surface area=1×1×6=6cm}}^{\text{2}}$

  ${\text{Volume of cube=1×1×1=6cm}}^{\text{3}}$

  $\text{Ratio of surface area to volume=6:1}$

Now if the cell grows larger to 2cm per side,

  $\text{Length of the cell=2cm}$

  ${\text{Surface area=2×2×6=24cm}}^{\text{2}}$

  ${\text{Volume of cube=2×2×2=8cm}}^{\text{3}}$

  $\text{Ratio of surface area to volume=24:8=3:1}$

The new ratio of 3:1 is less than 6:1. Therefore we can say that as the cell grows larger the ratio of surface area to volume decreases.