Answer: Third option
[tex]V_s=14\ m^3[/tex]
Step-by-step explanation:
The volume of a sphere is:
[tex]V_s=\frac{4}{3}\pi r^3[/tex]
Where r is the radius of the sphere
The volume of a cylinder is:
[tex]V_c = \pi r ^ 2 h[/tex]
Where h is the height of the cylinder and r is the radius
We assume that the height of the sphere is its diameter or 2 times its radius.
Then [tex]2r = h[/tex]
[tex]V_c= 21\ m^3=\pi r ^ 2 h[/tex]
[tex]V_c= 21\ m^3=\pi r ^ 2(2r)[/tex]
We solve the equation for r
[tex]\frac{21}{2\pi}=r ^ 3\\\\r= \sqrt[3]{\frac{21}{2\pi}}\\\\r=1.495\ m[/tex]
The radius of the cylinder is equal to the radius of the sphere
Finally
[tex]V_s=\frac{4}{3}\pi (1.495)^3[/tex]
[tex]V_s=14\ m^3[/tex]
