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Why are most organisms with exoskeletons relatively small? a. Increases in body weight increase body size by a factor of eight, and the chitin thickness of the exoskeleton has to significantly decrease to accommodate increase in body size. b. Doubling of body size increases body weight by a factor of eight, and the chitin thickness of the exoskeleton has to significantly decrease to accommodate weight increase. c. Increases in body weight increase body size by a factor of eight, and the chitin thickness of the exoskeleton has to significantly increase to accommodate increase in body size. d. Doubling of body size increases body weight by a factor of eight, and the chitin thickness of the exoskeleton has to significantly increase to accommodate weight increase.

Step by step solution

01

Understand the Problem

The problem is asking why most organisms with exoskeletons are relatively small. It is associated with the relationship between body size, body weight, and the thickness of the exoskeleton.

02

Analyze the Relationship between Body Size and Weight

According to the principles of geometry and biology, when an organism doubles in size, the volume and thus the weight increases by a factor of eight due to the cubic relationship (since volume is proportional to the cube of the linear dimensions).

03

Examine the Options

The options essentially relate to whether the chitin thickness of the exoskeleton increases or decreases, and how much the weight increases with doubling of body size. By understanding the previous step, the correct relationship should be: 'Doubling of body size increases body weight by a factor of eight'.

04

Consider the Structural Integrity of Exoskeletons

To maintain structural integrity, thicker exoskeletons would be required to support greater weight. Hence, if an organism's body weight increases by a factor of eight, the exoskeleton must significantly increase in thickness to support this weight.

05

Identify the Correct Answer

Among the options, the correct one must reflect that doubling body size increases body weight by a factor of eight, and thicker exoskeletons are necessary to accommodate increased weight.

06

Select the Correct Option

The correct answer is (d) because it matches both the increase in weight and the necessary increase in chitin thickness for structural support.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

chitin thickness

Chitin is a strong but lightweight material that composes the exoskeletons of many organisms like insects and crustaceans. It's made of long chains of a glucose derivative and serves both as a form of protection and structural support. However, there are limitations to how thick chitin can become. As an organism grows, the volume to be protected and supported increases exponentially. This means that for larger organisms, the chitin would need to be significantly thicker to provide the same level of support. Therefore, there's a practical limit to the size that an organism with an exoskeleton can achieve before the required chitin thickness becomes biologically unfeasible.

body size and weight relationship

The relationship between body size and weight is a critical factor in understanding why organisms with exoskeletons are small. When an organism's size doubles, its volume—and thus its weight—increases by a factor of eight (since volume is proportional to the cube of the linear dimensions). This exponential increase in weight requires the exoskeleton to bear much greater loads. As weight increases, the demands on the structure supporting that weight, in this case, the exoskeleton, increase disproportionately. So, small increases in body size result in much larger increases in body weight, placing tremendous strain on the organism's exoskeleton.

structural integrity

For an exoskeleton to effectively protect and support an organism, it must maintain structural integrity under the weight it bears. This means the exoskeleton needs to be thicker and robust enough to handle increased loads. As previously stated, an organism's weight increases radically with size due to its cubic relationship. Maintaining structural integrity requires disproportionately thicker exoskeletons for larger organisms. Therefore, there is a physical limitation to how large these organisms can grow while still being able to support their body weight with their exoskeleton. This need for thicker exoskeletons to manage increased weight is why most organisms with exoskeletons are relatively small.