Net of Cylinder
Introduction
A cylinder has traditionally been three dimensional solid, one of the most basic of curve linear. Cylinder has two circular bases and a curved lateral face.
Objective
To observe the net of cylinder.
User Guideline
Click and observe the slider of net of cylinder.
Test your outstanding
Given GGB applet is Net of ......................
Construction Protocol
Firstly we opem GGB applet .
Then we also choose 3D Graphics
Take a slider t (0,1,0.01) on 2D Graphic.
Again we choose input bar then choose following condition and click enter turn by turn.
1. A=Point(yAxis)
2. B=Point(yAxis)
3. c=Circle(A, B, xOyPlane)
4.θ =(1 - t) π
5.r=π / θ
6.ϕ= t π / 2
7.Take Cylinder(c,3) then enter and rename
8.C=Intersect(zAxis, e) [hints: join intersect point on cylinder top point and zAxis]
9.a=Line(C, xAxis)
10.D= (0, 1, 3)
11.g=PerpendicularLine(D, xOyPlane)
12.K=Circle(g, C)
13.e'=Rotate(Rotate(e, ϕ, a), ϕ, xAxis)
14.d=Rotate(Rotate(e, ϕ, a), ϕ, xAxis)
15.h=Circle(A, B, xOyPlane)
16.E=If(t < 1, (r sin(-θ), r (1 - cos(-θ)) cos(ϕ) - 3sin(ϕ), 3cos(ϕ) + r (1 - cos(-θ)) sin(ϕ)), (-π, -3sin(ϕ), 3cos(ϕ)))
17.F=If(t < 1, (r sin(θ), r (1 - cos(θ)) cos(ϕ) - 3sin(ϕ), 3cos(ϕ) + r (1 - cos(θ)) sin(ϕ)), (π, -3sin(ϕ), 3cos(ϕ)))
18.G=If(t < 1, (r sin(-θ), r (1 - cos(-θ)) cos(ϕ), r (1 - cos(-θ)) sin(ϕ)), (-π, 0, 0))
19.H=If(t < 1, (r sin(θ), r (1 - cos(θ)) cos(ϕ), r (1 - cos(θ)) sin(ϕ)), (π, 0, 0))
20. m=Segment(E, G)
21.n=Segment(F, H)
22.p=Line((0, 1, 0), zAxis)
23.q=Circle(p, B)
24.i=If(t < 1, Surface(r sin(u θ), r (1 - cos(u θ)) cos(ϕ) - v sin(ϕ), v cos(ϕ) + r (1 - cos(u θ)) sin(ϕ), u, -1, 1, v, 0, 3), Surface(π u, -v sin(ϕ), v cos(ϕ), u, -1, 1, v, 0, 3))
25.j=If(t < 1, Curve(r sin(u θ), r (1 - cos(u θ)) cos(ϕ), r (1 - cos(u θ)) sin(ϕ), u, -1, 1), Curve(π u, 0, 0, u, -1, 1))
26.k=If(t < 1, Curve(r sin(u θ), r (1 - cos(u θ)) cos(ϕ) - 3sin(ϕ), 3cos(ϕ) + r (1 - cos(u θ)) sin(ϕ), u, -1, 1), Curve(π u, -3sin(ϕ), 3cos(ϕ), u, -1, 1))
27.then we choose different colour
28. Hide other object and Show the figure net of cylinder.