$(8$ points$)$ Consider the figure below. A piece of gold is first weighed when fully submerged in some liquid, and then weighed again when outside of it$.$

a$)$ Calculate the buoyant force, $F_B.$

$F_B=17\mathrm{.}1N-16\mathrm{.}3N$

$=0\mathrm{.}80N$

b$)$ Using Archimedes' principle, determine the density of the displaced fluid, ${}_{df},$ that the piece of gold is submerged in$.$ Circle the correct fluid from the densities below. Use ${}_{\text{g}\text{o}\text{l}\text{d}}=19300k\frac{g}{m^3}$ for the density of submerged piece of gold. $($Hint: The object is fully submerged so the the volume of the fluid displaced is the same as the volume of the submerged piece of gold. Also, use the fact that $m_{\text{g}\text{o}\text{l}\text{d}}={}_{\text{g}\text{o}\text{l}\text{d}}{V}_{\text{g}\text{o}\text{l}\text{d}}).$ Show your work.