Problem $7.($Surface Area of Soil Particles$)$

Hint: Volume of sphere $=(\frac{4}{3})r^3$

Surface Area of Sphere $=4r^2$

Surface Area of Disk $=2R^2+2RT,h$ is thickness

Volume of Disk $=T{R}^2$

Calculate the specific surface $($area per unit mass$)$ of a spherical particle of

density $$ and radius $r.$

Calculate the specific surface $9$area per unit mass$)$ of disk shaped platelet of

density $,$ radius $R,$ and thickness $T.$

Calculate the specific surface area in centimeters squared per gram of the

following "idealized" soil particles:

a $2$ mm$-$diameter gravel sphere

a $0\mathrm{.}05-$mm$-$diameter sand sphere

a $0\mathrm{.}0022-$mm$-$diamter silt sphere

and a circular clay platelet of diameter $0\mathrm{.}002mm$ and a thickness ${10}^{-6}mm.$

For simplicity, assume that all the particles have the same mineral density $=2\mathrm{.}7$

$\frac{g}{c}{m}^3.$