Volume of Solids
The volume of the solid is 758.83 in³
Step-by-step explanation:
Given that the cone and half sphere is hollow
The volume of the cone = [tex]1/3 \pi r^{2} h\\[/tex]
The Volume of the sphere = [tex]4/3 \pi r^{3}[/tex]
So the Volume of the half sphere =[tex]2/3\pi r^{3}[/tex]
The volume of solid = volume of cone + volume of the half sphere
[tex]V = V_{1} + V_{2}[/tex]
Given
height h = 19 in
radius r = 5 in
[tex]V_{1\\}[/tex] = [tex]1/3 \pi r^{2} h[/tex]
= 1/3 × 3.14 × 5 × 5 × 19
= 497.16 in³
[tex]V_{2} = 2/3 \pi r^{3}[/tex]
= 2/3 × 3.14 × 5 × 5 × 5
= 261.67 in³
V = 497.16 in³ + 261.67 in³
= 758.83 in³
Hence the volume of the solid is 758.83 in³
