Question

1. for each statement below, circle which capitalized word/phrase correctly completes the sentence

a. as a cell gets larger, the ratio of surface area to volume increases or decreases (circle one).
b. larger or smaller (circle one) ratios are better for the cell.
c. as a cell gets larger, materials can diffusion in/out of a cell more quickly or more slowly (circle one).

1. use the picture below to determine if cell a, b, or c is the correct answer for each question

ratio of surface area to volume in cells
a. which cell has the highest sa:v ratio?
b. which cell has the lowest sa:v ratio?
c. which cell will be able to get needed materials in/out of the cell?
d. which cell cannot survive?
e. which cell is placing the highest demand on the dna?

1. a. what is asexual reproduction?

Explanation:

• 3a: The surface - area - to - volume ratio formula for a cube is \(SA/V=\frac{6s^{2}}{s^{3}}=\frac{6}{s}\) (where \(s\) is the side length). As \(s\) (cell size) increases, \(\frac{6}{s}\) decreases.
• 3b: A larger surface - area - to - volume ratio means more surface area relative to volume. This allows for more efficient exchange of materials (e.g., nutrients in, waste out) across the cell membrane.
• 3c: Since the surface - area - to - volume ratio decreases as the cell gets larger, the rate of diffusion (which depends on the surface area available for exchange relative to the volume that needs to be serviced) slows down.
• 4a: For cell A (\(s = 1\)cm), \(SA/V=\frac{6\times1^{2}}{1^{3}} = 6\). For cell B (\(s=2\)cm), \(SA/V=\frac{6\times2^{2}}{2^{3}}=\frac{24}{8}=3\). For cell C (\(s = 3\)cm), \(SA/V=\frac{6\times3^{2}}{3^{3}}=\frac{54}{27}=2\). So cell A has the highest ratio.
• 4b: Using the calculations above (\(SA/V\) for A = 6, B = 3, C = 2), cell C has the lowest ratio.
• 4c: The cell with the highest \(SA/V\) ratio (cell A) can exchange materials more efficiently.
• 4d: A cell with a very low \(SA/V\) ratio (cell C) cannot efficiently exchange materials (e.g., get enough nutrients in and waste out) to survive.
• 4e: A larger cell (cell C) has more volume (more cytoplasm, more organelles etc.) that needs to be regulated by the DNA. So it places a higher demand on the DNA.

Answer:

• 3a. DECREASES
• 3b. LARGER
• 3c. MORE SLOWLY
• 4a. Cell A
• 4b. Cell C
• 4c. Cell A
• 4d. Cell C
• 4e. Cell C