Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex ....

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Transcript of Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex ....

Page 2: Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex . base. A Cone is made by rotating a triangle . radius . height. h . r . r . h . base
Page 3: Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex . base. A Cone is made by rotating a triangle . radius . height. h . r . r . h . base

Geometry of Cones

Page 4: Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex . base. A Cone is made by rotating a triangle . radius . height. h . r . r . h . base

is a pyramid with

a flat base, curved wall

and pointy end

Cone in Geometry

Page 5: Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex . base. A Cone is made by rotating a triangle . radius . height. h . r . r . h . base

apex

base

Page 6: Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex . base. A Cone is made by rotating a triangle . radius . height. h . r . r . h . base

A Cone is made by rotating a triangle

radius

heig

ht

Page 7: Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex . base. A Cone is made by rotating a triangle . radius . height. h . r . r . h . base

h

r r

h

base area + side wall area = π r2 + π r s = π r (r + s)

end areas + side wall area = 2(π r2) + 2π r h

= 2π r (r + h)

Page 8: Geometry of Cones€¦ · a flat base, curved wall . and pointy end . Cone in Geometry . apex . base. A Cone is made by rotating a triangle . radius . height. h . r . r . h . base

volume base area X height

= π r2 h

cone’s volume = 1 3

cylinder’s volume 1

2 3