Which of the following accurately describes the relationship between an animal's surface area and its volume as it grows larger?
A
Volume increases faster than surface area.
B
Surface area and volume increase at the same rate.
C
Surface area increases faster than volume.
D
Surface area decreases while volume increases.
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1
Understand the concept of surface area to volume ratio: As an object grows, its volume increases faster than its surface area. This is because volume is a cubic function while surface area is a square function.
Consider the mathematical representation: For a cube with side length 'a', the surface area is given by the formula and the volume is given by .
Analyze the growth rates: As 'a' increases, the volume () increases more rapidly than the surface area ().
Apply this concept to biological organisms: Larger animals have a lower surface area to volume ratio compared to smaller animals, which affects their physiology, such as heat retention and metabolic rates.
Conclude with the correct relationship: Therefore, as an animal grows larger, its volume increases faster than its surface area.