Correct. Find the volume of each part and then add them together.

Volume of cylinder: $\displaystyle{V}=\pi{{r}}^{{2}}{h}=\pi{{\left({4}\right)}}^{{2}}{\left({7}\right)}=\pi{\left({16}\right)}{\left({7}\right)}\approx{3.14}\cdot{112}={351.68}\usepackage{cmbright}\Huge\$

Volume of cone: $\displaystyle{V}=\frac{{1}}{{3}}\pi{{r}}^{{2}}{h}=\frac{{1}}{{3}}\pi{{\left({4}\right)}}^{{2}}{\left({6}\right)}=\frac{{1}}{{3}}\pi{\left({16}\right)}{\left({6}\right)}\approx\frac{{{3.14}\cdot{96}}}{{3}}={100.48}\usepackage{cmbright}\Huge\$

Total volume: $\displaystyle{351.68}+{100.48}\approx{452}\usepackage{cmbright}\Huge\$ cubic inches