Question $6$

The table below shows point data collected from a topographic survey. Twenty$-$five points were considered.

Table $1$: Topographic data

$\backslash$table$[[$POINTID$,$Easting $[$m$],$Northing $[$m$],$Elevation $[$m$],$POINTID,Easting $[$m$],$Northing $[$m$],$Elevation $[$m$]],[$a$,0,0,1000\mathrm{.}000,$n$,30,20,1006\mathrm{.}980],[$b$,10,0,999\mathrm{.}630,0,40,20,1007\mathrm{.}080],[$c$,20,0,999\mathrm{.}050,$p$,40,30,1008\mathrm{.}850],[$d$,30,0,998\mathrm{.}480,$q$,30,30,1010\mathrm{.}070],[$e$,40,0,996\mathrm{.}030,$r$,20,30,1009\mathrm{.}980],[f,40,10,1002\mathrm{.}770,5,10,30,1010\mathrm{.}290],[$g$,30,10,1003\mathrm{.}770,t,0,30,1011\mathrm{.}980],[$h$,20,10,1006\mathrm{.}420,u,0,40,1014\mathrm{.}750],[$i$,10,10,1008\mathrm{.}600,v,10,40,1014\mathrm{.}230],[$j$,0,10,1008\mathrm{.}780,$w$,20,40,1004.100],[$k$,0,20,1010\mathrm{.}730,x,30,40,1003\mathrm{.}740],[1,10,20,1010\mathrm{.}400,$y$,40,40,1002\mathrm{.}270],[$m$,20,20,1008\mathrm{.}630,,,,]]$

a$)$ Using elevation data in table $1$ above, sketch a contour map of $2$ m interval. $[12$ marks$]$

b$)$ A vertical excavation is to be made within a closed polygon $\text{'}$c$-$e$-$o$-$m$-$c$\text{'}$ to a reduced level of $993\mathrm{.}53$ m $.$ Calculate the volume of earth to be excavated. $[8$marks$]$