Question

A cone of base diameter 40 mm and axis height 60 mm rests on the ground on a point of
its base circle such that the axis of the cone is inclined at 40° to the H.P and 30° to the
V.P, Draw its projections using auxiliary method​

Answer 1

Answer:

Given data

Diameter of cone = 40mm

Axis length = 60 mm

Resting on circular rim on HP

Axis inclination with HP = 40°

Top view of an axis is inclined 30° with VP

Stage 1

1. Draw XY line.
2. Cone is resting on HP, so TV will be a circle and FV will be a triangle.
3. Draw TV as a circle of diameter 40 mm.
4. Draw vertical and horizontal axis of circle.
5. Divide the circle into 12 equal parts (You can divide it into 8 parts also). Name all the points 1, 2, 3,….12.
6. Take the projections of all point into FV.
7. Complete the FV taking axis length 60 mm. Draw all the generators of cone.
8. Name the FV of cone on base as 1’ 2’ 3’….12’ and O’ as apex.

Stage 2

1. As axis is inclined at 30° to XY line the base line 1’7’ will be inclined at 60° to XY line.
2. So first mark point 7’ at some convenient distance on XY line. Then draw line 1’ 7’ at angle of 60°, so that the axis will be inclined at 30°.
3. Using compass mark all the points from stage 1 to stage 2 on line 1’ 7’.
4. Complete the FV in inclined position using compass.
5. Take the vertical projections of all 12 points 1’, 2’, 3’, …12’ and apex points O’ in TV.
6. Take horizontal projection all points along with apex towards right side from the TV of 1st stage.
7. Mark the intersection points 1,2,3..12 and apex O.
8. Draw a smooth curve passing through all the 12 points.
9. Join end generators with apex.

Stage 3

1. Now in third stage the top view of an axis is inclined to VP.
2. Draw a line inclined at angle of 30° to XY line.
3. Mark point O at some convenient distance below XY line.
4. Using compass complete the TV in inclined position
5. Take the projection all points along with apex into FV.
6. Take the projection all points along with apex towards right side from the FV of 2nd stage.
7. Mark intersection points 1’ 2’ 3’, ...12’ and apex O’
8. Draw a smooth curve passing through all the 12 points.
9. Join end generators with apex O.

Answer 2

Answer:

Projections using auxiliary method

Explanation:

Given

Diameter of cone = 40 mm

Axis length = 60 mm

Axis inclination with HP = 30

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