The figure given in the question is a composite figure, meaning that it comprises two different figures
The volume of the composite figure can be found as follow
The two figures are:
Cylinder and sphere.
To solve this, we will first find the area of a cylinder
[tex]\begin{gathered} \text{Area of a cylinder is given by:} \\ V_{\text{cylinder}}=\pi r^2h \\ \text{where} \\ \pi=3 \\ r=4 \\ h=6 \end{gathered}[/tex]So, we will have
[tex]\begin{gathered} V_{\text{cylinder}}=3\times4^2\times6 \\ V_{\text{cylinder}}=288\operatorname{cm}^3 \end{gathered}[/tex]Then, we will find the volume of the sphere
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\pi r^3 \\ \text{where} \\ \pi=3 \\ r=4 \end{gathered}[/tex]Thus, the volume of the sphere will be
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\times3\times4^3 \\ V_{\text{sphere}}=256\operatorname{cm}^3 \end{gathered}[/tex]Thus, the total volume will be
[tex]288+256=544\operatorname{cm}^3[/tex]The volume is:
[tex]544\operatorname{cm}^3[/tex]The answer is 544cm³