The volume of the hemisphere is calculated as follows:
[tex]V=\frac{2}{3}\pi r^3[/tex]where r is the radius of the hemisphere.
Since the diameter is 12 cm, then the radius is 12/2 = 6 cm. Substituting this value into the equation, the volume is:
[tex]\begin{gathered} V=\frac{2}{3}\cdot\pi\cdot6^3 \\ V=\frac{2}{3}\cdot\pi\cdot216 \\ V=144\pi \\ V=452.39\operatorname{cm}^3 \end{gathered}[/tex]The soup fills this volume. Given that 1 cubic centimer weighs 1.02 grams, then 452.39 cubic centimeter will weigh:
[tex]\begin{gathered} \frac{1\operatorname{cm}}{452.39\operatorname{cm}^3}=\frac{1.02\text{ grams}}{x\text{ grams}} \\ 1\cdot x=1.02\cdot452.39 \\ x=461.44\text{ grams} \end{gathered}[/tex]The bowl and the soup combined weigh 658.74 grams, the weight of the empty bowl is 658.74 - 461.44 = 197.3 grams.
