Sections of solids: a solved example
A cylinder of 60 mm base diameter and 80 mm axis rests on HP on its base with its axis perpendicular to HP. It is cut by a section plane perpendicular to VP and inclined at 30° to HP, bisecting the axis. Draw its front view, sectional top view and the true shape of the section.
Every line below was drawn and checked by Graspline's own geometry engine, by the textbook method, one step at a time with the reason for each.
The construction, step by step
Draw the reference line XY
Cylinder of 60 mm base diameter and 80 mm axis, resting on its base on HP, cut by a section plane perpendicular to VP and inclined at 30° to HP, bisecting the axis. The part between the plane and the observer is removed; the top view is drawn of what remains, with the cut surface hatched, and the true shape of the cut is projected on a plane parallel to the section plane.
The top view is the true shape of the base
The axis is perpendicular to HP, so the base lies in HP and the top view shows it in true shape (the two bases coincide). This is the view the section will be drawn in, so it is drawn in thin lines first and darkened where the solid remains.
Project the front view
Project every corner; the base is on XY and the axis is 80 mm high. These two views are the uncut solid.
Draw the section plane as its VT in the front view
The plane is perpendicular to VP, so in the front view it is a straight line — its vertical trace VT — at 30° to XY, bisecting the axis. Where it crosses an edge of the solid is a cut point: name them in order round the solid, with primes in this view.
Project the cut points and draw the sectional top view
Project each cut point to the edge it lies on in the top view and join them in order: that is the section. The removed part is left thin, the edges that remain are darkened with their visibility, and the cut surface is hatched at 45°.
The true shape of the section, on an auxiliary plane parallel to it
The section is seen edge-on in the front view, so its true shape is a view taken perpendicular to it: draw a fold X₁Y₁ parallel to the VT, project each cut point across it, and set it off at the distance its point in the top view stands from XY. Join in order.
Result
The front view with the VT, the sectional top view, and the true shape of the section.
Section points12True shape: longest side17.8 mmSection area3117.7 mm²✓ Verified: every cut point lies on the section plane and on its edge; every side of the true shape is the true length of that side of the section.
Draw your own question in Graspline →
Free while we test it.
Graspline is not affiliated with any university or examination board. Terms of use