Given:
A figure of combination of hemisphere, cylinder and cone.
Radius of hemisphere, cylinder and cone = 6 units.
Height of cylinder = 12 units
Slant height of cone = 10 units.
To find:
The volume of the given figure.
Solution:
Volume of hemisphere is:
[tex]V_1=\dfrac{2}{3}\pi r^3[/tex]
Where, r is the radius of the hemisphere.
[tex]V_1=\dfrac{2}{3}(3.14)(6)^3[/tex]
[tex]V_1=\dfrac{6.28}{3}(216)[/tex]
[tex]V_1=452.16[/tex]
Volume of cylinder is:
[tex]V_2=\pi r^2h[/tex]
Where, r is the radius of the cylinder and h is the height of the cylinder.
[tex]V_2=(3.14)(6)^2(12)[/tex]
[tex]V_2=(3.14)(36)(12)[/tex]
[tex]V_2=1356.48[/tex]
We know that,
[tex]l^2=r^2+h^2[/tex] [Pythagoras theorem]
Where, l is length, r is the radius and h is the height of the cone.
[tex](10)^2=(6)^2+h^2[/tex]
[tex]100-36=h^2[/tex]
[tex]\sqrt{64}=h[/tex]
[tex]8=h[/tex]
Volume of cone is:
[tex]V_3=\dfrac{1}{3}\pi r^2h[/tex]
Where, r is the radius of the cone and h is the height of the cone.
[tex]V_3=\dfrac{1}{3}(3.14)(6)^2(8)[/tex]
[tex]V_3=\dfrac{25.12}{3}(36)[/tex]
[tex]V_3=301.44[/tex]
Now, the volume of the combined figure is:
[tex]V=V_1+V_2+V_3[/tex]
[tex]V=452.16+1356.48+301.44[/tex]
[tex]V=2110.08[/tex]
Therefore, the volume of the given figure is 2110.08 cubic units.
