$2-$ In a sand cone test using a standard sand of $=1\mathrm{.}5\frac{g}{c}{m}^3,$ a test hole was dug and weight of excavated soil was found to be $2040$ g while its water content was $4\%.$ The weight of the sand cone device filled with the standard before and after the test was $8160$ g and $4490$ g $,$ respectively. Given that the volume of cone $=1230c{m}^3$ and ${}_{\text{d}\text{m}\text{a}\text{x}}$ in the lab compaction test $=1\mathrm{.}7\frac{g}{c}{m}^3,$ find the percent compaction $($relative compaction$)$ of the tested soil.