The figure attached is composed of a cylinder and an sphere. Then:
Surface Area = Total Area of the Sphere + Side Area of the Cylinder.
Hence:
[tex]\begin{gathered} A_{sphere}=4πr^2 \\ A_{sphere}=4\times\pi\times8^2 \\ A_{sphere}=804.25cm^2 \end{gathered}[/tex]
Now, the side area of the cylinder:
[tex]\begin{gathered} SA_{cylinder}=2\timesπ\times r\times h \\ SA_{cylinder}=2\timesπ\times8\times12.5 \\ SA_{cylinder}=628.32cm^2 \end{gathered}[/tex]
Finally:
[tex]SA=804.25+628.32=1432.57cm^2[/tex]
ANSWER
The surface area is 1432.6 cm²
Now, to find the volume:
Total Volume = Volume of the Sphere + Volume of the Cylinder
Volume of the Sphere:
[tex]\begin{gathered} V_{sphere}=\frac{4}{3}πr³ \\ V_{sphere}=\frac{4}{3}\pi\times8^3=2144.66cm^3 \end{gathered}[/tex]
Volume of the Cylinder:
[tex]\begin{gathered} V_{cylinder}=πr²h \\ V_{cylinder}=π\times8^2\times12.5=2513.27cm^3 \end{gathered}[/tex]
Finally:
[tex]V=2144.66+2513.27=4657.93cm^3[/tex]
ANSWER
The volume is 4657.9cm³
