EXPLANATION
The area of a circle is given by the following relationship:
[tex]\text{Area}_{\text{circle}}=\pi\cdot r^2[/tex]
Where r=radius= diameter/2
Replacing terms:
[tex]254.5=\pi\cdot r^2[/tex]
Dividing pi to both sides:
[tex]\frac{254.5}{\pi}=r^2[/tex]
Applying the square root to both sides:
[tex]r=\sqrt[]{\frac{254.5}{\pi}}[/tex]
Simplifying:
[tex]r=\sqrt[]{81}=9[/tex]
As the diameter=2*radius ----> Diameter = 18 units
