The volume of the given shape is required.
The required volume is 282.74 in³.
Volume
d = Diameter = 6 inches
r = Radius = d/2 = 6/2 = 3 inches
h = Height = 8 inches
The given figure is made of a hemisphere and cylinder
Volume of a cylinder is given by [tex]\pi r^2h[/tex]
Volume of a hemisphere is given by [tex]\dfrac{2}{3}\pi r^3[/tex]
The total volume is
[tex]V=\pi r^2h+\dfrac{2}{3}\pi r^3\\\Rightarrow V=\pi r^2\left(h+\dfrac{2}{3}r\right)\\\Rightarrow V=\pi\times 3^2\left(8+\dfrac{2}{3}\times 3\right)\\\Rightarrow v=90\pi=282.74\ \text{in}^3[/tex]
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