A cylinder has traditionally been three dimentional solid, one of the most basic of curvilinerar. Cylinder has two circular bases and a curved lateral face.

To observe the net of cylinder.

Check the GGB applet. Click and observe the slider of net of cylinder. what did you find?

Firstly we opem GGB applet .[br]Then we also choose 3D Graphics[br]Take a slider t (0,1,0.01) on 2D Graphic.[br]Again we choose input bar then choose following condition and click enter turn by turn.[br]1. A=Point(yAxis)[br]2. B=Point(yAxis)[br]3. c=Circle(A, B, xOyPlane)[br]4. [math]\theta[/math]=(1 - t) π[br]5.r=π / θ[br]6.[math]\phi[/math]= t π / 2[br]7.Take Cylinder(c,3) then enter and rename [br]8.C=Intersect(zAxis, e) [hints: join intersect point on cylinder top point and zAxis][br]9.a=Line(C, xAxis)[br]10.D= (0, 1, 3)[br]11.g=PerpendicularLine(D, xOyPlane)[br]12.K=Circle(g, C)[br]13.e'=Rotate(Rotate(e, ϕ, a), ϕ, xAxis)[br]14.d=Rotate(Rotate(e, ϕ, a), ϕ, xAxis)[br]15.h=Circle(A, B, xOyPlane)[br]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)))[br]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)))[br]18.G=If(t < 1, (r sin(-θ), r (1 - cos(-θ)) cos(ϕ), r (1 - cos(-θ)) sin(ϕ)), (-π, 0, 0))[br]19.H=If(t < 1, (r sin(θ), r (1 - cos(θ)) cos(ϕ), r (1 - cos(θ)) sin(ϕ)), (π, 0, 0))[br]20. m=Segment(E, G)[br]21.n=Segment(F, H) [br]22.p=Line((0, 1, 0), zAxis)[br]23.q=Circle(p, B)[br]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))[br]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))[br]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))[br]27.then we choose different colour [br]28. Hide other object and Show the figure net of cylinder.[br]