If you unfurl the lateral "face" of a cone, you get the sector of a circle whose central angle subtends an arc with length 
equal to the circumference of the cone's base, and a radius equal to the slant height 
of the cone.
Since the diameter of the base is 18m, the circumference of the base is about
meters, so this is the value of .
You're given a slant height of
meters.
Now, the following proportional relation holds for any circle:
This translates to
(remember, we're talking about a sector of a circle with radius and arc length 
). Solving for 
:
So the area of the lateral face is approximately 4.5 square meters.
Since the diameter of the base is 18m, the circumference of the base is about
You're given a slant height of
Now, the following proportional relation holds for any circle:
This translates to
(remember, we're talking about a sector of a circle with radius
So the area of the lateral face is approximately 4.5 square meters.