교과서 질문
Eukaryotic cells differ from prokaryotic cells in that only eukaryotic cells .a. contain DNA;b. have a plasma membrane;c. are considered to be alive;d. have a nucleus;e. are able to evolve
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2. Cell Chemistry & Cell Components
Prokaryotic & Eukaryotic Cells
2:12 minutesProblem 15
교과서 질문
Imagine a spherical cell with a radius of 10 μm. What is the cell's surface area in μm2? Its volume, in μm3? (Note: For a sphere of radius r, surface area = 4πr2 and volume = 4/3πr3. Remember that the value of π is 3.14.) What is the ratio of surface area to volume for this cell? Now do the same calculations for a second cell, this one with a radius of 20 μm. Compare the surface-to-volume ratios of the two cells. How is this comparison significant to the functioning of cells?
검증된 단계별 안내1
Step 1: Calculate the surface area of the first cell using the formula for the surface area of a sphere: \( \text{Surface Area} = 4\pi r^2 \). Substitute \( r = 10 \mu m \) into the formula.
Step 2: Calculate the volume of the first cell using the formula for the volume of a sphere: \( \text{Volume} = \frac{4}{3}\pi r^3 \). Substitute \( r = 10 \mu m \) into the formula.
Step 3: Determine the surface area to volume ratio for the first cell by dividing the surface area by the volume.
Step 4: Repeat Steps 1 to 3 for the second cell with \( r = 20 \mu m \). Calculate its surface area, volume, and surface area to volume ratio.
Step 5: Compare the surface area to volume ratios of the two cells and discuss the significance. Consider how a larger surface area to volume ratio might affect cellular processes such as nutrient uptake and waste removal.
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2mTextbookSolutions.keyConceptsTitle
TextbookSolutions.keyConceptsSubtitle
Surface Area and Volume Formulas
The surface area and volume of a sphere are calculated using specific mathematical formulas: surface area = 4πr² and volume = 4/3πr³. These formulas are essential for determining the physical properties of spherical objects, such as cells, which are often modeled as spheres in biological contexts. Understanding these formulas allows for the calculation of how much surface area is available for processes like nutrient absorption and waste elimination.
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The surface-to-volume ratio (SA:V) is a critical concept in biology that describes the relationship between the surface area of a cell and its volume. A higher SA:V ratio indicates that a cell has more surface area relative to its volume, which is advantageous for efficient exchange of materials with the environment. This ratio influences cellular functions, growth, and the ability to maintain homeostasis, making it a key factor in cell size and shape.
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Cell size is significant in biology because it affects metabolic rates, nutrient uptake, and waste removal. Smaller cells typically have a higher surface-to-volume ratio, facilitating more efficient transport of substances across their membranes. As cells grow larger, their SA:V ratio decreases, which can limit their ability to function effectively, leading to the necessity for specialized structures or division to maintain optimal cellular function.
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