Answer:
The diameter of the sphere is 6 centimeters
Step-by-step explanation:
we know that
The surface area of a sphere is
[tex]SA=4\pi r^{2}[/tex]
The volume of the sphere is
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
Equate both formulas
[tex]\frac{4}{3}\pi r^{3}=4\pi r^{2}[/tex]
Simplify
[tex]\frac{1}{3}r^{3}=r^{2}[/tex]
[tex]\frac{r^3}{r^2}=3[/tex]
[tex]r=3\ cm[/tex]
Remember that the diameter is two times the radius
so
[tex]D=2r=2(3)=6\ cm[/tex]
therefore
The diameter of the sphere is 6 centimeters
