Rather simple question

1. May 23, 2009

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

2. May 23, 2009

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:

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

3. May 23, 2009

ronaldor9

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

4. May 23, 2009

ryan88

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