ANSWER :
A. The area of Circle K is about 500 cm^2 greater than the area of Circle J.
EXPLANATION :
Recall the area formula of a circle :
[tex]A=\pi r^2[/tex]
Note that the radius is half of diameter.
The diameter of Circle J is 18 cm so the radius is 18/2 = 9 cm
The diameter of Circle K is 31 cm so the radius is 31/2 = 15.5 cm
The areas are :
[tex]\begin{gathered} \text{ Circle J :} \\ A=(3.14)(9)^2=254.34cm^2 \\ \text{ Circle K :} \\ A=(3.14)(15.5)^2=754.385cm^2 \end{gathered}[/tex]
The area of Circle K is greater than Circle J by 754.385 - 254.34 = 500.045 cm^2 or 500 cm^2