Table of contents

1. Introduction to Biology2h 42m
2. Chemistry3h 37m
3. Water1h 26m
4. Biomolecules2h 23m
5. Cell Components2h 26m
6. The Membrane2h 31m
7. Energy and Metabolism2h 0m
8. Respiration2h 40m
9. Photosynthesis2h 49m
10. Cell Signaling59m
11. Cell Division2h 47m
12. Meiosis2h 0m
13. Mendelian Genetics4h 44m
14. DNA Synthesis2h 27m
15. Gene Expression3h 6m
16. Regulation of Expression3h 31m
17. Viruses37m
- Viruses
  37m
18. Biotechnology2h 58m
19. Genomics17m
- Genomes
  17m
20. Development1h 5m
21. Evolution3h 1m
22. Evolution of Populations3h 53m
23. Speciation1h 37m
24. History of Life on Earth2h 6m
25. Phylogeny2h 31m
26. Prokaryotes4h 59m
27. Protists1h 12m
28. Plants1h 22m
29. Fungi36m
- Fungi
  19m
- Fungi Reproduction
  17m
30. Overview of Animals34m
- Overview of Animals
  34m
31. Invertebrates1h 2m
32. Vertebrates50m
33. Plant Anatomy1h 3m
34. Vascular Plant Transport1h 2m
- Water Potential
  1h 2m
35. Soil37m
- Soil and Nutrients
  20m
- Nitrogen Fixation
  16m
36. Plant Reproduction47m
- Flowers
  33m
- Seeds
  14m
37. Plant Sensation and Response1h 9m
38. Animal Form and Function1h 19m
39. Digestive System1h 10m
- Digestion
  1h 3m
- Blood Sugar Homeostasis
  7m
40. Circulatory System1h 49m
41. Immune System1h 12m
42. Osmoregulation and Excretion50m
- Osmoregulation and Excretion
  50m
43. Endocrine System1h 4m
- Endocrine System
  1h 4m
44. Animal Reproduction1h 2m
- Animal Reproduction
  1h 2m
45. Nervous System1h 55m
- Neurons and Action Potentials
  1h 8m
- Central and Peripheral Nervous System
  46m
46. Sensory Systems46m
- Sensory System
  46m
47. Muscle Systems23m
- Musculoskeletal System
  23m
48. Ecology3h 11m
49. Animal Behavior28m
- Animal Behavior
  28m
50. Population Ecology3h 41m
51. Community Ecology2h 46m
52. Ecosystems2h 36m
53. Conservation Biology24m
- Conservation Biology
  24m

5. Cell Components

Prokaryotic & Eukaryotic Cells

General Biology

5. Cell Components

Prokaryotic & Eukaryotic Cells

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2:12 minutes

Problem 15

Textbook Question

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?

Verified step by step guidance

Step 1: Start by calculating the surface area of the first cell (radius = 10 μm). Use the formula for the surface area of a sphere:

A = 4 π r^{2}

. Substitute r = 10 μm into the formula.

Step 2: Next, calculate the volume of the first cell using the formula for the volume of a sphere:

V = \frac{4}{3} π r^{3}

. Substitute r = 10 μm into the formula.

Step 3: Determine the surface area-to-volume ratio for the first cell by dividing the surface area by the volume:

\frac{A}{V}

. Use the values calculated in Steps 1 and 2.

Step 4: Repeat Steps 1 through 3 for the second cell, which has a radius of 20 μm. Use the same formulas for surface area and volume, substituting r = 20 μm.

Step 5: Compare the surface area-to-volume ratios of the two cells. Discuss the significance of the comparison in terms of cell function, such as nutrient exchange and waste removal, emphasizing how smaller cells have a higher surface area-to-volume ratio, which is advantageous for efficient transport processes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 characteristics of spherical cells, which are common in biological systems. Understanding these calculations allows for insights into how cells interact with their environment.

Surface Area-to-Volume Ratio

The surface area-to-volume ratio (SA:V) is a critical concept in biology that describes how the surface area of a cell relates to its volume. A higher SA:V ratio indicates that a cell has more surface area relative to its volume, which facilitates efficient nutrient uptake and waste removal. This ratio is crucial for understanding cellular efficiency and limits on cell size.

Biological Implications of Cell Size

Cell size has significant biological implications, particularly regarding metabolic rates and the efficiency of transport processes. Smaller cells tend to have higher SA:V ratios, allowing for more effective exchange of materials with their environment. This concept is vital for understanding how cell size influences growth, function, and overall organismal physiology.

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