Question

introduction to cells
key ideas
as you read this section, keep these questions in mind:

• how were cells discovered?
• what defines cell shape and size?
• why can eukaryotes perform more specialized functions than prokaryotes can?

how were cells discovered?
most cells are too small to see with the eye alone.
before the microscope was invented, no one knew about cells. in 1665, an english scientist named robert hooke used a crude microscope to look at a thin slice of cork. the microscope made the image 30 times larger. he saw many little boxes in the cork, which he called cells.
as different scientists used better microscopes to look at more objects, they realized three major points. together, these points are known as the cell theory.

• all living things are made up of one or more cells.
• cells are the basic units of structure and function in organisms.
• all cells come from existing cells.

what defines the size and shape of a cell?
cells vary in size and shape. human body cells range from 5 to 20 μm in diameter. bacteria cells are even tinier. why are cells so small?
anything that enters or leaves a cell must pass through the cells surface. therefore, a cells size is limited by the cells surface area - to - volume ratio.
as a cell gets larger, its surface area - to - volume ratio gets smaller even though it must take up more nutrients and remove more wastes.

Explanation:

Step1: Calculate volume of large cube

Volume of a cube \( V = s^3 \), where \( s = 4\) mm. So \( V=4^3=64\) mm³.

Step2: Calculate surface area of large cube

Surface area of a cube \( SA = 6s^2 \). So \( SA = 6\times4^2=6\times16 = 96\) mm².

Step3: Calculate volume of small cubes

There are 8 small cubes. Volume of one small cube \( V_{small}=2^3 = 8\) mm³. Total volume \( V_{total}=8\times8 = 64\) mm³.

Step4: Calculate surface area of small cubes

Surface area of one small cube \( SA_{small}=6\times2^2=24\) mm². Total surface area \( SA_{total}=8\times24 = 192\) mm².

Answer:

• For the large cube: Volume is \( 64\) mm³ and surface area is \( 96\) mm².
• For the small cubes: Total volume is \( 64\) mm³ and total surface area is \( 192\) mm².