Answer:
Option B is correct
[tex]20 m^3[/tex]
Step-by-step explanation:
Volume of the sphere(V) is given by:
[tex]V = \frac{4}{3} \pi r^3[/tex]; .....[1] where, r is the radius of the sphere.
Volume of cylinder(v') is given by:
[tex]V'= \pi r'^2h'[/tex]
where, r' is the radius of the cylinder and h' is the height of the cylinder
As per the statement:
A sphere and a cylinder have the same radius and height.
r = r'
h = 2r = h'
It is also given that: The volume of the cylinder is 30 m^3
⇒[tex]V' = \pi r'^2h'[/tex]
⇒ [tex]30 = \pi r^2 \cdot (2r)[/tex]
⇒ [tex]30 = 2 \pi r^3[/tex]
Divide both sides by 2 we have;
[tex]15 = \pi r^3[/tex]
Substitute in [1] we have;
[tex]V = \frac{4}{3} \cdot 15[/tex]
Simplify:
[tex]V = 20 m^3[/tex]
Therefore, volume of sphere is, [tex]20 m^3[/tex]
