Respuesta :
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.
Explanation:
One sand granule when placed on the paper, will cover the area "a" which is given as:
[tex]\begin{gathered} a=\pi(\frac{d}{2})^2 \\ \\ a=\pi\times(\frac{0.0062\text{ cm}}{2})^2 \\ \\ a=\pi\times(0.0031\text{ cm})^2 \\ \\ a=3.01907\times10^{-5}\text{ cm}^2 \end{gathered}[/tex]The area "A" of the given paper can be calculated as:
[tex]\begin{gathered} A=l\times b \\ \\ A=28\text{ cm}\times22\text{ cm} \\ \\ A=616\text{ cm}^2 \end{gathered}[/tex]Now, the number of salt grains "N" needed to cover the paper can be calculated as:
[tex]\begin{gathered} N=\frac{A}{a} \\ \\ N=\frac{616\text{ cm}^2}{3.01907\times10^{-5}\text{ cm}^2} \\ \\ N=20403634.23 \\ \\ N\approx20403634 \end{gathered}[/tex]Final answer:
20403634 salt granules are required to cover the area of the given paper.
