Question

Size (diameter) of one salt granule is 0.062 mm measured with micrometer. How many grains (grains as granules, not unit of measurement) of salt are needed to cover piece of paper with lenght 28 cm and width 22 cm? The only tool provided is a ruler. The salt particles are very fine and difficult to count individually. Thank you!

Answer 1

Given:

The diameter of one salt granule is: d = 0.062 mm = 0.0062 cm.

The length of the paper is: l = 28 cm

The width of the paper is: b = 22 cm

To find:

A number of salt grains are needed to cover the paper of the given dimensions.

Step-by-step explanation:

One sand granule when placed on the paper, will cover the area "a" which is given as:

`\begin{gathered} a=\pi((d)/(2))^2 \\ \\ a=\pi*(\frac{0.0062\text{ cm}}{2})^2 \\ \\ a=\pi*(0.0031\text{ cm})^2 \\ \\ a=3.01907*10^(-5)\text{ cm}^2 \end{gathered}`

The area "A" of the given paper can be calculated as:

`\begin{gathered} A=l* b \\ \\ A=28\text{ cm}*22\text{ cm} \\ \\ A=616\text{ cm}^2 \end{gathered}`

Now, the number of salt grains "N" needed to cover the paper can be calculated as:

`\begin{gathered} N=(A)/(a) \\ \\ N=\frac{616\text{ cm}^2}{3.01907*10^(-5)\text{ cm}^2} \\ \\ N=20403634.23 \\ \\ N\approx20403634 \end{gathered}`

Final answer:

20403634 salt granules are required to cover the area of the given paper.