Question

1. determine the surface area to volume ratio for the cubes that have the following side lengths. which cube would represent the more efficient cell? explain your answer

a. 8 mm
b. 10 mm

Explanation:

Step1: Recall the formulas

Surface area of a cube \(S = 6s^{2}\), volume of a cube \(V=s^{3}\), ratio \(R=\frac{S}{V}=\frac{6s^{2}}{s^{3}}=\frac{6}{s}\)

Step2: Calculate for \(s = 8\space mm\)

Substitute \(s = 8\) into \(R=\frac{6}{s}\), we get \(R_{1}=\frac{6}{8}=\frac{3}{4}= 0.75\)

Step3: Calculate for \(s = 10\space mm\)

Substitute \(s = 10\) into \(R=\frac{6}{s}\), we get \(R_{2}=\frac{6}{10}=0.6\)

Step4: Determine the more efficient cell

A cell with a higher surface - area - to - volume ratio is more efficient as it can exchange materials (nutrients, waste) more effectively. Since \(0.75>0.6\)

Answer:

a. The surface - area - to - volume ratio is \(0.75\)
b. The surface - area - to - volume ratio is \(0.6\)
The cube with side length \(8\space mm\) represents the more efficient cell because it has a higher surface - area - to - volume ratio, which allows for more efficient exchange of materials (such as nutrients in and waste out) across its surface.