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BIOLOGY 100
SOLUTIONS TO PROBLEMS
CELL STRUCTURE
1. A cell is 8 µm in width and depth, and 30 µm in length. What is the surface area of this cell? What
is the volume of this cell? What is the surface area to volume ratio of this cell?
Consider the geometry of this cell:
Surface Area = surface area of 2 ends + surface area of 4 sides
= 2 x (8 µm x 8 µm) + 4 x (8 µm x 30 µm) = 1,088 µm2
Volume = base x height x depth
= 8 µm x 8 µm x 30 µm = 1,920 µm3
Surface Area to Volume ratio = Surface Area ÷ Volume
= 1,088 µm2 ÷ 1,920 µm3 = 0.57 µm-1
2. If a cubical cell maintained its shape while it grew to ten times its initial size, by what percent
would the surface to volume ratio change?
The original cell is a cube and has sides with the dimension of 1 arbitrary unit (units are not
shown below).
Surface Area of original cell = total surface area of the six panels that form the cube
= 6 x (1 x 1) = 6
Volume of original cell = side3 = 13 = 1 x 1 x 1 = 1
Surface Area : Volume of original cell = 6 ÷ 1 = 6
The enlarged cell is also a cube but has sides ten times larger.
Surface Area of enlarged cell = 6 x (10 x 10) = 600
Volume of enlarged cell = 103 = 1,000
Surface Area : Volume of enlarged cell = 600 ÷ 1,000 = 0.6
Comparison of Surface Area : Volumes = SA : V enlarged = 0.6 = 0.1
SA : V original 6
Hence, the SA : V for the enlarged cell is only 0.1 (10%) of the original.
8 µm
8 µm
30 µm
Note: 1 is the same as µm-1
µm
