We have been given that a sphere and a cylinder have the same radius and height.
We know that height of sphere is equal to its radius. So [tex]h=r[/tex].
Now we will use volume of sphere and volume of cylinder formula to solve our given problem.
Volume of cylinder: [tex]V=\pi r^2h[/tex], where,
r = Radius,
h = Height
Volume of sphere: [tex]V=\frac{4}{3}\pi r^3[/tex], where,
r = Radius.
Since height is equal to radius, so we will get:
[tex]V=\pi r^2\cdot r=\pi r^3[/tex]
Since volume of cylinder is [tex]18[/tex] cubic cm, so we will equate volume formula with [tex]18[/tex] as:
[tex]\pi r^3=18[/tex]
Let us solve for r.
[tex]\frac{\pi r^3}{\pi}=\frac{18}{\pi}[/tex]
[tex]r^3=\frac{18}{\pi}[/tex]
[tex]r=\sqrt[3]{\frac{18}{\pi}}[/tex]
Upon substituting this value in volume of sphere formula, we will get:
[tex]V=\frac{4}{3}\pi\cdot \left(\sqrt[3]{\frac{18}{\pi}}\right)^3[/tex]
[tex]V=\frac{4}{3}\pi\cdot \frac{18}{\pi}[/tex]
[tex]V=\frac{4}{1}\cdot 6[/tex]
[tex]V=24[/tex]
Therefore, the volume of the sphere would be 24 cubic cm and option B is the correct choice.