Surface Area of Cone

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The complete the following activities


Define the points
A = (0, 0, 3)
B = (3, 0, 0)
O = (0, 0, 0)
Hide the objects A.B and O

Define a point
P=Point(Segment(A, O))
Hide the label

Define circle, points and angles
c:=Circle(P, Distance(A, B), yAxis)
C & D:= Intersect(xOyPlane, c)
α:=2π x(B) / x(D)
γ:=π - α / 2
Hide objects c,C,D,α,γ


Define slope
f(x):=(-z(P)) / x(D) (x - x(D))
hide f(x)

Define cone as a surface
cone:=Surface(u cos(v), u sin(v), f(u), u, 0, x(D), v, γ, 2π - γ)
Hide the label

Rotate the point D
R:=Rotate(D, γ, zAxis)
S:=Rotate(D, -γ, zAxis)
Hide the points R and S

Define arcs
arc1:=CircumcircularArc(R, C, S)
Set caption 2πr
arc2:=CircumcircularArc(S, D, R)
Conditional visibility
arc1≠0
Hide the label

Define Circle
fullarc:=Circle(zAxis, D)
Conditional visibility
arc1=0
Hide the label

Define Segments
l:=segment(P,R)
s2:=segment(P,S)
Hide s2