Answer
$2.84\ ft$
Work Step by Step
1.find total volume of 1 mol sand grain and divide by area of Texas to get height. Pay attention to Units:
Volume of 1 cubical sand grain= $(0.10mm)^3= 1.0\times 10^{-3} \ mm^3 $
1 mole =$6.023\times10^{23}$
Total volume of sand = $(6.023\times10^{23})\times(1.0\times10^{-3} mm^3)
= 6.023\times10^{20} mm^3 $
Convert to ft:
1inch=25.4 mm so 12in (1 ft) = 12 x 25.4 mm = 304.8 mm
Express volume of sand in $ft^3$
$(6.023\times10^{20} mm^3)\times((1 ft)^3)/((304.8mm)^3) = 2.127\times10^{13} ft^3 $
Convert miles to ft -- 1 mile =5280 ft
Finally divide volume of sand by area:
Height
=$\frac{2.127\times 10^{13} ft^3}{(268,601 miles^2))\times((1 mile^2)/(5280^2 ft^2)} $
Height =$2.84\ ft$
