Given:
The radius of the cone = 14 ft
The slant height of the cone = 27 ft
To find the lateral surface area and the total surface area of the given cone.
Formula
The lateral surface area of the cone is
and
The total surface area of the cone is
where,
r be the radius and
l be the slant height of the cone.
Now
Taking r = 14 and l = 27 we get
sq ft
or, 
sq ft
Again,
sq ft
or,
sq ft
Hence,
The lateral surface area of the cone is 1187.5 sq ft and the total surface area of the cone is 1803.3 sq ft. Option C.
The answer is: The first triangle. The reasons are shown below:
1. All the triangles are rigth triangles, because they have an angle of 90°. So, let's calculate the others angles of the first one:
Tan(α)^-1= opposite leg/adjacent leg
Opposite leg=5
Adjacent leg=5√3
Tan(α)^-1= 5/5√3
Tan(α)^-1=30°
2. Let's calculate the other angle:
Tan(α)^-1= opposite leg/adjacent leg
Now, the opposite leg will be 5√3 and the adjacent leg will be 5. Then:
Tan(α)^-1= 5√3/5
Tan(α)^-1=60°
As you can see, the angles of first triangle are: 30°,60° and 90°.
Since we have a transverse line that cuts through the straight line parallel to the height, then we can see that the angles are divided into two sections.
We also have vertically opposite angles, since the angle sum of a straight line is 180°. We have perpendicular lines since we are given a 90° angle. Thus, we know the missing angle is 45°.
Thus, 45 + x = 180
x = 135°
3x3 -4= 5 5(-1)= -5 -5(-4)= 20
