Question

If the diameter of a cell is 40 micrometers, what is the scale factor for making a model cell where 1 cm corresponds to 0.5 micrometers?

a) 0.025
b) 0.5
c) 2
d) 40

Answer 1

None of the given options is correct.

Step-by-step explanation:

To determine the model scale factor, we need to compare the actual size with the model size. If 1 cm on the model represents 0.5 micrometers of the actual cell, and the actual diameter of the cell is 40 micrometers, then the model scale factor can be calculated as follows:

First, convert the actual diameter of the cell to the same units as the model: 40 micrometers is 40 × 10-6 meters, or 40 × 10-4 centimeters (since 1 meter is 100 centimeters).

Given the model scale of 1 cm = 0.5 micrometers, we can set up a proportion to calculate the scale factor:

1 cm (model) / 0.5 μm (actual) = X cm (model) / 40 μm (actual)

Cross-multiply to solve for X:

0.5 μm × X cm = 1 cm × 40 μm

X = 1 cm × 40 μm / 0.5 μm = 80 cm

Therefore, to represent an actual cell diameter of 40 micrometers, the model will be 80 centimeters in diameter. This means the scale factor is 80 (since 80 cm represents what would actually be 40 micrometers in real life).