Problem 4 - Campbell Biology

Question

Compared with a smaller cell, a larger cell of the same shape has (A) less surface area. (B) less surface area per unit of volume. (C) the same surface-area-to-volume ratio. (D) a smaller cytoplasm-to-nucleus ratio.

Step-by-Step Solution

Answer

The answer is (B) less surface area per unit of volume.

Step 1: Understanding Surface Area and Volume

The surface area of a cell is proportional to the square of its linear dimensions, and the volume is proportional to the cube of its linear dimensions.

Step 2: Comparing Surface Area

For a larger cell, the surface area is greater because surface area increases with the square of the cell's dimensions.

Step 3: Comparing Volume

For a larger cell, the volume is also greater because volume increases with the cube of the cell's dimensions.

Step 4: Surface-Area-to-Volume Ratio

As the cell becomes larger, its volume increases faster than its surface area. Therefore, the surface area per unit volume decreases.

Step 5: Answer Analysis

Based on the steps above, a larger cell of the same shape has less surface area per unit of volume compared to a smaller cell.

Key Concepts

surface area

Surface area is a key concept in understanding cell biology. It can be thought of as the total area that covers the surface of the cell. For any given shape, the surface area is proportional to the square of its dimensions. For example, if a cell's dimension is doubled, its surface area increases by a factor of four (since surface area ∝ length²). This concept is essential in biology because the surface area of a cell is where many critical processes occur, such as the exchange of materials, including nutrients, gases, and waste products, between the cell and its environment.

volume

Volume refers to the amount of space inside the cell. It is proportional to the cube of the cell's dimensions. If the cell’s dimension doubles, its volume increases by a factor of eight (since volume ∝ length³). This rapid increase in volume compared to surface area creates a significant biological challenge. Because the cell's internal volume grows much faster than its surface area as the cell becomes larger, processes that rely on surface exchange, such as nutrient uptake and waste removal, become less efficient.

cell size impact

The impact of cell size is crucial in cell biology. As cells grow larger, their surface-area-to-volume ratio decreases. This means that for a larger cell, there is less surface area available per unit of volume. Consequently, larger cells may struggle more with efficiently exchanging materials through their surface compared to smaller cells. This imbalance is why most cells remain small, optimizing their surface-area-to-volume ratio to maintain efficient function. In the given exercise, a larger cell compared to a smaller one has less surface area per unit of volume, highlighting this key point. This concept is vital for understanding cell growth, function, and the limitations that cells face as they increase in size.