$1.$ You are given a truckload containing $2$ cubic meters of quartz gravel, each cobble of the load is a sphere $10$ cm in diameter. To get to your house, the truck has travelled down a very bumpy road, and the jostling has caused the load to settle into a closest packing fabric.

a$.$ What would you estimate the porosity of the gravel to be$?$

b$.$ Given this porosity, what is the weight of this load of rocks?

c$.$ Approximately how many cobbles are in this truckload?

d$.$ If these cobbles were broken down into sand grains with an average grain diameter of $1$ mm$,$ what would be the volume of the resulting load of sand? Assume that the new load of sand weighs the same $($e$.$g$.$ no loss of quartz during abrasion$)$

e$.$ What is the weight and volume of a load of sand having the same number of sand grains as cobbles in the original load?