A cone of base diameter 50 mm and axis height 65 mm is resting on HP on one of its generators with axis parallel to VP. It is cut by A.I.P. such that the true shape of the section is a parabola with the axis length equal to 60 mm. Draw the projection of cut solid and also draw the development of lateral surface of the remaining part of the cone.

**Given Data:**

Cone Diameter = 50 mm

Axis Length = 65 mm

Resting on HP with one of its generators with axis is parallel to VP.

True shape of section is parabola having axis length 60 mm (The length of section line is 60 mm) Procedure –

**Stage 1: FV and Sectional TV**

Draw XY line.

As the cone is resting on Hp, the TV will be a circle.

Draw a circle of 50 mm diameter. Draw vertical and horizontal axis of the circle.

Divide the circle into 12 equal parts and name it 1, 2, 3 ...12 and apex O.

Take the projection all points and apex in FV, starting from XY line measure axis length 50 mm and complete the FV. Name the FV as 1’2’3’ ...12’ on base and O’ as apex.

For drawing AIP, taking 60 mm (axis of parabola) as radius and 7’ as center cut the end generator O’7’. Mark that point P7’

Draw a section plane passing through point P7’ and parallel to end generators O’1’

It will cut the base, mark that point ab.

Section line will cut the cone at different points such as if it cuts on end generators O’1’ name it P1’, on end generators O’2’ name it P2’ etc. and if it cuts on base then name it a’ and b’.

Take the projection of P1’, P2’, P3’...P12’ and a’ and b’ in TV. Mark point P1, P2, P3...P12 on end generators O 1, O 2, O 3 ...O 12 in TV respectively. Also mark a and b between point 2 and 3 and 11 and 12 respectively.

Join point a and b with straight line whereas other points through smooth curve. This parabolic part is the removed part of the cone. Show it by hatching line.

**Stage 2: True Shape of Section**

Draw the section line on left side of FV (take the measurement from FV a’b’ to P7’).

Mark all points on section line using compass such as P1, P2’, P3’...P12’ and a’b’.

Take the projection of above points in TV, below XY line.

From sectional TV take the projections of P1, P2, P3..P12 and a and b towards left side.

Mark the intersection points and join all these points as a smooth curve.

True shape of section (TSS) is parabola in shape.

**Stage 3: Development**

On the right side of FV take the projection of apex O’ at some convenient distance. From that point draw a line parallel to O’7’. Say O 1.

Taking O1 as radius and O as center draw an arc of angle θ (θ = (r/L)*360) (where r = radius of cone and L = length of end generator O’7’) and divide it into 12 equal using protractor (Development).

Joint all the points with apex O, O1, O2, O3....O12.

Take the projection of point P1’P2’ P3’.... P12’ on line O1.

As Centre and OP7’ as radius draw an arc, it will intersect generator O7. Mark that point P7.Repeat the same procedure for all the points mark the points P3, P4, P5, P6, P8, P9, P10 and P11.

Mark point a and b on circumference as per shown in diagram using compass.

Draw a smooth curve passing through all above points.