Assignment 15: Net of cylinder

Introduction

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.

Objectives

To observe the net of cylinder.

User guideline

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

Net of cylinder

Some questions

1. How many circular face in cylinder?

Select all that apply

Construction protocal

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.

=(1 - t) π 5.r=π / θ 6.

= 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.