An object is suspended from a mass balance. When the object is surrounded by air, the mass balance reads $210$ g $.$ When the object is completely submerged in water, the mass balance reads $175$ g $.($the density of water is $1\mathrm{.}0\frac{g}{c}{m}^3)$

a$)$ What is the volume of the object $($in $c{m}^3)?$

b$)$ What is the density of the object $($in $\frac{g}{c}{m}^3)?$