Multiple Choice
Which of the following structures is found in eukaryotic cells but not in prokaryotic cells?
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5. Cell Components
Prokaryotic & Eukaryotic Cells
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How does the size of a cell's surface area change compared to its volume as the cell grows?
A
The surface area increases faster than the volume.
B
The surface area increases at the same rate as the volume.
C
The surface area decreases while the volume increases.
D
The surface area increases slower than the volume.
Verified step by step guidance1
Understand the relationship between surface area and volume as a cell grows. The surface area is related to the square of the radius, while the volume is related to the cube of the radius.
Consider the mathematical expressions for surface area and volume. For a spherical cell, the surface area \( A \) is given by \( A = 4\pi r^2 \) and the volume \( V \) is given by \( V = \frac{4}{3}\pi r^3 \).
Analyze how these formulas change as the radius \( r \) increases. The surface area increases with the square of the radius, while the volume increases with the cube of the radius.
Compare the rates of increase: since the cube function grows faster than the square function, the volume of the cell increases at a faster rate than the surface area as the cell grows.
Conclude that as a cell grows, its surface area increases slower than its volume, which can affect the cell's ability to efficiently exchange materials with its environment.
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