The cone shown has a diameter of 18 meters and a slant height of 15 meters. which choice is closest to the lateral surface area? use 3.14 to approximate pi.

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.