When given this kind of composite figures, what we have to do is split it into individual figures. In this case, we would have a cylinder and half a sphere.
For the cylinder:
Remember that the formula for the volume of a cylinder is:
[tex]V_c=\pi r^2h[/tex]
Where r is the radius of the base and h is the height of the cylinder.
Using this and the data given, we get that:
[tex]V_c=\pi(3^2)(10)\rightarrow V_c=282.74[/tex]
The volume of the cyllinder is 282.74 cubic inches.
For the semisphere:
Remember that the formula for the volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Now, notice that we have half a sphere, so the formula we'll use is:
[tex]V_s=\frac{4}{6}\pi r^3[/tex]
This way,
[tex]V_s=\frac{4}{6}\pi(3^3)\rightarrow V_s=56.55[/tex]
Adding up both volumes,
[tex]282.74+56.55=339.29[/tex]
This way, the volume of the composite figure, rounded to the nearest hundredth is 336.29 cubic inches
