Vertex of cone surrounded by filter paper:
Fold the filter paper twice and divide it into four parts. Now there are three overlapping parts, so the perimeter of these three layers only accounts for 1 point of the four parts, plus the other half 1 layer, so the perimeter of the cone bottom circle is half of that before folding:1/2 * 2π r =1/2 * π.
Radius of base circle =5π/2π=5/2 bus = radius of great circle =5.
On the cross section, within the right triangle surrounded by the height, radius and generatrix of the cone: radius/generatrix = 1/2.
So: the vertex angle of the triangle =30 degrees.
The vertex angle of the triangle on the cross section of the cone =2*30=60 degrees.
Similarly, the funnel radius/generatrix =3/6= 1/2, then the funnel vertex angle is 60 degrees.
So they can overlap!
2, S fan = (LR)/2 (L is the arc length of the sector)
Funnel center angle =L/ circumference *360 degrees
L=2πR=2π* 1/2*7.2=7.2π
Perimeter =2πR=2π*6= 12π
Funnel central angle =7.2π/ 12π*360 degrees =2 16 degrees.
S fan = (n/360) π * r * r (n is the degree of central angle)
s fan =(2 16/360)π* 5 * 5 = 15π。
S circle =πR*R=π*5*5=25π.
S circle -S fan =25π- 15π= 10π.
The extra area is folded in half and overlapped on the cone, so that together with the original layer, * * * is three layers.
So the area of each layer in the overlapping part = 1/2* 10π=5π.
5π is approximately equal to 5*3. 14= 15.7.