Answer:
12 cm³
Step-by-step explanation:
Let's say the radius of the sphere and cylinder is r and the height is h. However, notice that the "height" of the sphere is the same thing as the diameter, which is 2r, so h = 2r.
The volume of a sphere is denoted by: [tex]V=\frac{4}{3} \pi r^3[/tex] , where r is the radius.
The volume of a cylinder is denoted by: [tex]V=\pi r^2h[/tex], where r is the radius and h is the height. Plug in 2r for h and 18 for V:
[tex]V=\pi r^2h[/tex]
[tex]18=\pi r^2*2r=2\pi r^3[/tex]
[tex]\pi r^3=18/2=9[/tex]
Now plug in 9 for πr³ in the volume formula for the sphere:
[tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} *9=12[/tex]
The volume of the sphere is 12 cm³.
