Answer:
[tex]V=169.56\ mm^3[/tex]
Step-by-step explanation:
we know that
The volume of the cone is given by te formula
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]V=113.04\ mm^3[/tex]
substitute
[tex]113.04=\frac{1}{3}\pi r^{2}h[/tex]
[tex]339.12=\pi r^{2}h[/tex] ----> equation A
Remember that
A sphere has the same height and a circular base with the same diameter
That means----> The diameter of the sphere is equal to the height of the cone and the radius of the sphere is equal to the radius of the base of cone
[tex]r=\frac{h}{2}[/tex]
equation A is equal to
[tex]339.12=\pi (\frac{h}{2})^{2}h[/tex]
[tex]339.12=\pi (\frac{h^3}{3})[/tex]
[tex]1,017.36=\pi h^3[/tex] -----> equation B
The volume of the sphere is given by
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
substitute
[tex]V=\frac{4}{3}\pi (\frac{h}{2})^{3}[/tex]
[tex]V=\frac{4}{24}\pi h^3[/tex]
[tex]V=\frac{1}{6}\pi h^3[/tex]
substitute equation B in the expression above
[tex]V=\frac{1}{6}(1,017.36)=169.56\ mm^3[/tex]
