Question

explore
directions: read the information below and then answer the questions.
many factors influence cell growth and division, including cell size. a typical animal cell only grows to
a size of 10 - 20 micrometers. cell size is often expressed as a comparison of two quantities: surface area
and volume. a cells surface area - to - volume ratio is the relationship between the surface area of a cells
membrane and the inner volume of the cell.
a ratio is a comparison of two numbers. for example, suppose there are 25 students in a class: 10 boys
and 15 girls. the ratio of boys to girls is 10 to 15. we can express this ratio in one of three ways.
10 to 15 10:15 10/15
a ratio can be reduced, just like any other fraction. ratios are reduced by determining the lowest common
denominator. in the example above, the greatest common factor is 5.
10/15 = 2/3 = 2:3
study the image below. it can also be found on page 225 in your textbook. in the image, the first cell is
cell a, the second is cell b, and the third is cell c.
example: calculate the surface area - to - volume ratio for cell a.
· surface area = length x width x number of sides = 1 x 1 x 6 = 6
· volume = length x width x height = 1 x 1 x 1 = 1
· surface area - to - volume ratio = 6:1

1. calculate the surface area of cell b and cell c.
2. calculate the volume of cell b and cell c.
3. calculate the surface area - to - volume ratio for cell b and cell c.

Explanation:

Step1: Calculate surface area of Cell B

Surface area formula for cube \(SA = 6s^{2}\), where \(s = 2\).
\(SA=6\times2^{2}=6\times4 = 24\)

Step2: Calculate surface area of Cell C

Using \(SA = 6s^{2}\), with \(s = 3\).
\(SA=6\times3^{2}=6\times9 = 54\)

Step3: Calculate volume of Cell B

Volume formula for cube \(V=s^{3}\), \(s = 2\).
\(V = 2^{3}=8\)

Step4: Calculate volume of Cell C

Using \(V=s^{3}\), \(s = 3\).
\(V=3^{3}=27\)

Step5: Calculate surface - area - to - volume ratio for Cell B

Ratio \(=\frac{SA}{V}=\frac{24}{8}=3:1\)

Step6: Calculate surface - area - to - volume ratio for Cell C

Ratio \(=\frac{SA}{V}=\frac{54}{27}=2:1\)

Answer:

1. Surface area of Cell B: \(24\), Surface area of Cell C: \(54\)
2. Volume of Cell B: \(8\), Volume of Cell C: \(27\)
3. Surface - area - to - volume ratio for Cell B: \(3:1\), Surface - area - to - volume ratio for Cell C: \(2:1\)