Question

task d: whats the scale?
an epidemiologist (a scientist who studies diseases that affect people) makes a scale drawing of a white blood cell, which is about 20 micrometers (0.000020 meters) across.
partner a

1. write two possible scales the epidemiologist could have used if her drawing is 5 centimeters across.
2. the nucleus of the cell is about 8 micrometers across. how long would this be in her drawing?

partner b

1. write two possible scales the epidemiologist could have used if her drawing is 4 centimeters across.
2. the nucleus of the cell is about 10 micrometers across. how long would this be in her drawing?

359

Explanation:

Step1: Convert units

We know that 1 centimeter = 0.01 meters and 1 micrometer = 0.000001 meters. So 20 micrometers = 0.000020 meters and 1 centimeter = 100000 micrometers.

Step2: Calculate scale for Partner A - part 1

If the actual size of the white - blood cell is 20 micrometers and the drawing size is 5 centimeters (500000 micrometers), the scale is the ratio of the drawing size to the actual size. Let the scale be \(d:a\).
The first possible scale: If we simplify the ratio \(\frac{500000}{20}=25000:1\). Another way is to write it as 1 micrometer represents \(\frac{5}{0.00002}=250000\) micrometers or 250 millimeters or 25 centimeters. So another scale could be 1: \(\frac{1}{25000}\) (where 1 unit on the drawing represents \(\frac{1}{25000}\) units in real - life).

Step3: Calculate length in drawing for Partner A - part 2

If the scale is 25000:1 and the actual size of the nucleus is 8 micrometers, then the length in the drawing \(l = 8\times25000=200000\) micrometers = 20 centimeters.

Step4: Calculate scale for Partner B - part 1

If the actual size of the white - blood cell is 20 micrometers and the drawing size is 4 centimeters (400000 micrometers), the scale is \(\frac{400000}{20}=20000:1\). Another scale could be 1: \(\frac{1}{20000}\).

Step5: Calculate length in drawing for Partner B - part 2

If the scale is 20000:1 and the actual size of the nucleus is 10 micrometers, then the length in the drawing \(l=10\times20000 = 200000\) micrometers = 20 centimeters.

Answer:

Partner A:

1. 25000:1, 1:\(\frac{1}{25000}\)
2. 20 centimeters

Partner B:

1. 20000:1, 1:\(\frac{1}{20000}\)
2. 20 centimeters