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.