The surface area of a cone is equal to the base plus the lateral area.
The base is a circle, and has a diameter of 16 meters.
The radius is always half the diameter, so it is 8 meters.
The area of a circle = πr², where r is the radius. π(8)² = 64π ≈ 201.06193
The area of the base is ≈ 201.06193.
To find the lateral area of the cone, we need to find the slant height.
Since the height, radius, and slant height of the cone form a right triangle, we can use the Pythagorean Theorem to find the slant height with what we are given.
radius² + height² = slant height²
8² + 37² = slant height²
64 + 1369 = slant height²
1433 = slant height²
slant height = √1433
The lateral area of a cone is equal to πrl, where r = radius and l = slant height.
πrl = π(8)(√1433) ≈ 951.39958
(there are other formulas which do the same thing, but it doesn't matter.)
Now we add the lateral area and base together to find our surface area.
201.06193 + 951.39958 = 1152.46151 which rounds to C. 1,152 m².
