We have the following:
To calculate the volume of the figure, we must divide the figure into two parts, a cylinder and a cone
The volume of the cylinder is as follows
[tex]\begin{gathered} V_1=\pi\cdot r^2\cdot h \\ r=\frac{d}{2}=\frac{7}{2} \\ \text{replacing} \\ V_1=\frac{22}{7}\cdot\mleft(\frac{7}{2}\mright)^2\cdot15 \\ V_1=577.5 \end{gathered}[/tex]The volume of the cone is as follows
[tex]\begin{gathered} V_2=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ \text{replacing} \\ V_2=\frac{1}{3}\cdot\frac{22}{7}\cdot(\frac{7}{2})^2\cdot6 \\ V_2=77 \end{gathered}[/tex]The total volume is:
[tex]\begin{gathered} V_T=V_1+V_2 \\ V_T=577.5+77 \\ V_T=654.5 \end{gathered}[/tex]The answer is 654.5 cm^3