Given:
Radius of half sphere and cone = 6 cm
Height of cone = 12 cm
To find:
The volume of composite figure that is made up of a cone and a half sphere.
Solution:
Volume of half sphere is:
[tex]V_1=\dfrac{2}{3}\pi r^3[/tex]
Where r is the radius of the half sphere.
Putting [tex]\pi =3.14, r=6[/tex], we get
[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 a cone is:
[tex]V_2=\pi r^2h[/tex]
Where r is the radius and h is the height of the cone.
Putting [tex]\pi =3.14, r=6, h=12[/tex], we get
[tex]V_2=(3.14)(6)^2(12)[/tex]
[tex]V_2=(3.14)(36)(12)[/tex]
[tex]V_2=1356.48[/tex]
Volume of the composite figure is:
[tex]V=V_1+V_2[/tex]
[tex]V=452.16+1356.48[/tex]
[tex]V=1808.64[/tex]
Therefore, the volume of a composite figure is 1808.64 cubic centimetres.
Note: All options are incorrect.
