Answer:
The volume of the composite solid is [tex]1206.4(ft^{3})[/tex]
Step-by-step explanation:
The composite solid is formed by a cone and a cylinder.
The cone has 16 ft of diameter and its height is 6 ft. Also, its radius is 8 ft (half of the diameter).
The cylinder has 16 ft of diameter and its height is 4 ft. Also, its radius is 8 ft.
Given a cone of radius ''R'' and height ''h'' we can calculate its volume as :
[tex]V(cone)=\pi .R^{2}.\frac{1}{3}.h[/tex] (I)
Given a cylinder of radius ''R'' and height ''h'' we can calculate its volume as :
[tex]V(cylinder)=\pi .R^{2}.h[/tex] (II)
We can calculate the volume of the composite solid as the sum of the volume from the cone and the cylinder ⇒
[tex]V(CompositeSolid)=V(cone)+V(cylinder)[/tex]
If we apply (I) and (II) ⇒
[tex]V(CompositeSolid)=\pi .(8ft)^{2}.(\frac{1}{3}).(6ft)+\pi .(8ft)^{2}.(4ft)[/tex]
[tex]V(CompositeSolid)=128\pi (ft^{3})+256\pi (ft^{3})[/tex]
[tex]V(CompositeSolid)=384\pi (ft^{3})[/tex]
[tex]V(CompositeSolid)=1206.4(ft^{3})[/tex]
We find that the volume of the composite solid rounded to the nearest tenth is [tex]1206.4(ft^{3})[/tex]
