Rather simple question

[ronaldor9]

Suppose a poppy seed is .5 mm in diameter and holds ten thousand grains of sand. Find the diameter of each grain of sand? Im reading this book and the stated answer seems wrong.
thanks

 

[ryan88]

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

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

The volume of a grain of sand is given by:

$$V_s=\frac{V_p}{10000}=\frac{6.5\times 10^{-11}}{10000}=6.5\times 10^{-15}\text{m}^3$$

The diameter of a grain of sand is given by:

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

 

[ronaldor9]

yeah thats what ive been geting, the book is wrong it had it as 0.025 mm!

 

[ryan88]

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