Rather simple question

Assuming the poppy seed to be spherical, its volume is given by:

[tex]V_p=\frac{\pi}{6}d^3=\frac{\pi}{6}(0.5\times 10^{-3})=6.5\times 10^{-11}\text{m}^3[/tex]

The volume of a grain of sand is given by:

[tex]V_s=\frac{V_p}{10000}=\frac{6.5\times 10^{-11}}{10000}=6.5\times 10^{-15}\text{m}^3[/tex]

The diameter of a grain of sand is given by:

[tex]d_s=\sqrt[3]{\frac{6V_s}{\pi}}=2.3\times 10^{-5}\text{m}[/tex]

 

They are the same order of magnitude, the difference could just be due to rounding errors