Solving the Poppy Seed and Sand Diameter Puzzle

[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? I am 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 that's what I've 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