This document discusses sections of cones and provides examples of drawing sections of cones cut by different planes. It begins by explaining that the true shape of a cone section can be a circle, ellipse, parabola, hyperbola, or triangle depending on how the cutting plane intersects the cone. It then provides five examples of drawing front, top, and true shape views of cones cut by various planes, and explains how to determine the true shape in each case. The document concludes by providing tips for drawing cone sections, such as how the true shape is affected by the orientation of the cutting plane.

1. SECTIONS OF SOLIDS
Part II
Prof.T.JEYAPOOVAN
Department of Mechanical Engineering
Hindustan Institute of Technology and Science
Chennai-603103, India
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2. REFERENCE BOOKS
1. Jeyapoovan T, “Lesson Plans for Engineering
Graphics”, 2010, Vikas Publishing House Pvt
Ltd, New Delhi.
2. Jeyapoovan T, “Engineering Drawing and
Graphics”, 2011, Vikas Publishing House Pvt
Ltd, New Delhi.
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3. SECTION OF CONE
• When a cone is cut by a
section plane, the true
shape of section will be a
circle/ellipse/parabola/
hyperbola/triangle.
• Considering equal number
of generators (say 8), the
true shape of section is
obtained as discussed
earlier.
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4. Example 1: A cone of base diameter 50 mm and axis length 75 mm,
resting on HP on its base is cut by a plane inclined at 45° to HP and
perpendicular to VP and is bisecting the axis. Draw the front view and
sectional top view and true shape of this section.. Draw its front view,
sectional top view and true shape of section.
• Draw TV, project FV of cone and
assume 8 generators. Draw the
trace of cutting plane at 45º to XY.
• Mark the new corners in front view
and project them to top view to get
apparent section.
• Draw new reference line X1Y1 and
use the distance of new corners in
TV from XY and mark from X1Y1
and join them to get the true shape
of section as an ellipse.
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5. Example 2: A cone of base diameter 60 mm and axis length 80 mm is
resting on HP on its base. It is cut by a plane perpendicular to VP and
parallel to a contour generator and is bisecting the axis. Draw the front
view, sectional top view and the true shape section.
• Draw TV and project FV, assume
8 generators. Draw trace of the
cutting plane parallel the extreme
generator and passing through the
midpoint of the axis.
• Mark new corners in FV and
project them to TV.
• Draw new reference line X1Y1 and
use the distance of new corners in
TV from XY and mark from X1Y1
and join them to get the true
shape of section as a parabola.
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6. Example 3: A cone of base diameter 60 mm and axis length 70 mm is
resting on HP on its base. It is cut by a plane inclined at 45° to VP and
perpendicular to HP that cuts the cone at a distance 10 mm from the
axis and in front of it. Draw its top view, sectional front view and true
shape of section.
• Draw TV, project FV and assume
8 generators. Draw trace of the
cutting plane at 45º to XY and
10mm away from axis (i.e. centre
of circle in TV).
• Mark new corners in TV and
project them to FV.
• Draw new reference line X1Y1 and
use distance of new corners in FV
from XY and mark from X1Y1 and
join them to get the true shape of
section as a hyperbola.
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7. Example 4: A pentagonal pyramid of base side 30 mm and axis length
60 mm is resting on HP on its base with a side of base parallel to VP. It
is cut by a plane inclined at 45° to VP and perpendicular to HP and is 12
mm away from the axis. Draw its top view, sectional front view and true
shape of section.
• Draw TV and project FV. Draw
trace of the cutting plane which
touching a circle of radius 12mm
with the centre of the pentagon.
• Mark new corners in TV and
project them to FV.
• Draw new reference line X1Y1 and
use the distance of new corners in
FV from XY and mark from
X1Y1 , then join them to get the
true shape of section. www.engineeringgraphics.in

8. Example 5: A cube of 60 mm side has its base edges equally inclined to
VP. It is cut by a sectional plane perpendicular to VP, so that the true
shape of cut section is a regular hexagon. Locate the plane and
determine the angle of inclination of the VT with the reference line xy.
Draw the sectional top view.
• Draw TV and project FV of cube.
Note that in TV, two sides are taken
equally inclined to XY. Draw trace of
cutting plane passing through the
midpoint of six edges as shown.
• Mark the new corners in front view
and project them to top view.
• Draw new reference line X1Y1 and use
the distance of new corners in TV
from XY and mark from X1Y1,, then
join them to get the true shape of
section as a hexagon.
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9. Tips to draw Section of a Cone
• Draw the projections of the cone, then draw the trace of the
cutting plane. Carefully mark the new corners on the
generators cut by the cutting plane, then project them to the
other view.
• When a cone is resting on HP on its base and the cutting
plane is inclined to HP and perpendicular to VP, cuts all
generators, the true shape obtained will be an ellipse.
• When the cutting plane is inclined to HP and perpendicular
to VP cuts a few generators and also cuts the base of cone,
the true shape obtained will be a parabola.
• When the cutting plane parallel to the axis of the cone, true
shape obtained will be a hyperbola.
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10. End of Lesson 8
Thank You
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