The lateral area of a cone is the surface area (aka area of the sides of the object) minus the area of the base of the cone.
The equation for the lateral area of a cone is: [tex]lateral \: area = \pi rl[/tex]
where r = radius and l = slant height.
Since you know that the lateral area = [tex]500 \pi \: cm^{2} [/tex] and the radius, r = 50 cm, you can plug those values into the equation for the lateral area and solve for l, the slant height:
[tex]lateral \: area = \pi rl\\
500 \pi = \pi (50)(l)\\
500 = 50l\\
l = 10[/tex]
The slant height of the cone is A) 10cm.
