\[\boxed{\mathbf{6.115}}\]
\[\textbf{а)}\ \ масса\ 1\ дм^{3}\ вещества:\]
\[\frac{9}{16}\ :\frac{3}{4} = \frac{9}{16} \cdot \frac{4}{3} = \frac{3}{4}\ (г).\]
\[\textbf{б)}\ объем\ 1\ кг =\]
\[= 1000\ г\ вещества:\]
\[1000 \cdot \frac{3}{4}\ :\frac{9}{16} = \frac{1000 \cdot 3 \cdot 16}{4 \cdot 9} =\]
\[= \frac{1000 \cdot 4}{3} = \frac{4000}{3} =\]
\[= 1333\frac{1}{3}\ дм^{3}.\]