The volume of the composite figure is given by
Volume = Volume of Hemisphere + Volume of Cylinder
Volume of Hemisphere
This can be calculated by
[tex]V_1=\frac{2}{3}\pi r^3[/tex]
The radius is 3 ft (half of the diameter)
Hence,
[tex]\begin{gathered} V_1=\frac{2}{3}\times\pi\times3^3 \\ V_1=56.55 \end{gathered}[/tex]
Volume of Cylinder
This can be calculated by
[tex]V_2=\pi r^2h[/tex]
The radius is 0.75 ft (half of the diameter)
The height is 6 ft
Hence,
[tex]\begin{gathered} V_2=\pi\times0.75^2\times6 \\ V_2=10.60 \end{gathered}[/tex]
Therefore, the volume of the composite figure will be calculated by
[tex]\begin{gathered} V=V_1+V_2 \\ =56.55+10.60 \\ =67.15 \end{gathered}[/tex]
The volume of the composite figure is 67.15 cubic feet.
The SECOND OPTION is correct!
