WOLFRAM|DEMONSTRATIONS PROJECT

Cone, Tent, and Cylinder

radius r

height h

solid

cone

tent

cylinder

hide lines

Part

:Part specification

1,1,3,2,1 is longer than depth of object.

Part

:Part specification 1〚1〛 is longer than depth of object.

Part

:Part specification 1〚3〛 is longer than depth of object.

General

:Further output of Part::partd will be suppressed during this calculation.

Part

:The expression 1〚1〛 cannot be used as a part specification.

Part

:Part 2 of {},{},DirectiveOpacity[1.],AbsoluteThickness[1.6],FaceForm[Opacity[0.3]],

,Line[{{2.,0.},{2.,0.00385407},{1.99999,0.00770813},45,{1.96394,0.378076},{1.96315,0.382178},834}] does not exist.

Part

:Part 2 of {},{},DirectiveOpacity[1.],AbsoluteThickness[1.6],FaceForm[Opacity[0.3]],

,Line[{{2.,0.},{2.,0.00385407},{1.99999,0.00770813},45,{1.96394,0.378076},{1.96315,0.382178},834}] does not exist.

Part

:Part 2 of {},{},DirectiveOpacity[1.],AbsoluteThickness[1.6],FaceForm[Opacity[0.3]],

,Line[{{2.,0.},{2.,0.00385407},{1.99999,0.00770813},45,{1.96394,0.378076},{1.96315,0.382178},834}] does not exist.

General

:Further output of Part::partw will be suppressed during this calculation.

Append

:Nonatomic expression expected at position 1 in Append[1,0].

Append

:Nonatomic expression expected at position 1 in Append[1,0].

Append

:Nonatomic expression expected at position 1 in Append[1,0].

General

:Further output of Append::normal will be suppressed during this calculation.

Part

:The expression Polygon[{{1〚1〛〚1,1〛,0,3},Append[1,0],Append[1,0],{1〚1〛〚2,1〛,0,3},{1〚1〛〚1,1〛,0,3}}] cannot be used as a part specification.

The tent is formed by joining the points along a ridge line to a circle below. The lines joining the ridge to the circle lie in the plane perpendicular to the ridge.

The cone is formed by joining a point to the base circle and the cylinder joins the points of an elevated circle to the base circle, so the tent is in some sense in between those two more familiar solids.

Another intermediate property is that the cone, tent, and cylinder have volumes

, and

The horizontal cross sections of the tent are ellipses; the cross sections perpendicular to the ridge are isosceles triangles with base

2sin(r)

and constant height