### Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

### More or Less?

Are these estimates of physical quantities accurate?

### Time to Evolve

How many generations would link an evolutionist to a very distant ancestor?

# Biology Measurement Challenge

##### Age 14 to 16 Challenge Level:

The average dimension for each of the following objects is given in the table below:

 Length Cross - Sectional Area Volume Modelling by which solid? Mitochondria 1 $\mu$m 0.79 $\mu$m$^2$ 0.79 $\mu$m$^3$ Cylinder Arabis voch pollen 30 $\mu$m 706.9 $\mu$m$^2$ 14137 $\mu$m$^3$ Sphere Ring stage of Plasmodium falciparum 1.5 $\mu$m 0.79 $\mu$m$^2$ 0.03 $\mu$m$^3$ Ring Tuberculosis bacterium 2 $\mu$m 0.12 $\mu$m$^2$ 0.24 $\mu$m$^3$ Cylinder Human red blood cell 8 $\mu$m 50 $\mu$m$^2$ 100 $\mu$m$^3$ Disc Human nerve cell 2 $\mu$m 3 $\mu$m$^2$ 0.3 $\mu$m$^3$ Disc The eye of a needle 1 mm 1 mm$^2$ 0.1 mm$^3$ Cuboid Cat hair 3 cm 0.3 mm$^2$ 9 mm$^3$ Cylinder Snowflake crystal 1 cm 0.79 cm$^2$ 0.17 cm$^3$ Sphere

Therefore, we can roughly rank these objects by length, volume and cross - sectional area.