A hexagonal pyramid 35 mm side of base and 65 mm axis length rest on its base on the HP with one of its side of base perpendicular to VP. It is cut by section plane whose H.T. makes an angle $30^0$ with the XY and its 15 mm away from the axis of the pyramid. Draw the TV, sectional FV and the development of the lateral surface. Also draw the true shape of section.

Q. 6

Given Data

Side of pyramid = 35 mm

Axis length = 65 mm

Resting on HP with one of its side perpendicular to VP.

Horizontal Trace (HT) of Section plane is 15 mm away from axis.

Procedure –

Stage 1 – Sectional FV and TV

1. Draw XY line.

2. One of the base side of pyramid is perpendicular to VP and it is resting on HP. So TV will be a hexagon.

3. Draw the hexagon of 35 mm side as per shown in diagram.

4. Name all corner points and apex 1 2 3 4 5 6 and O.

5. Join all corner points with apex showing slant edges in TV.

6. Take the projection all corner points and apex in FV, starting from XY line measure axis length 65 mm and complete the FV. Name the FV as 1’2’3’4’ 5’ 6’ for base and O’ for apex.

7. For drawing HT of section plane, Taking O (in TV) as centre and 15 mm as radius draw a circle. It is given in the problem that HT is 15 mm away from the axis.

8. Draw a tangent line to that circle as shown in diagram.

9. Mark the intersection point of HT with TV as a, b, P3 and P4

10. Take the projection of all above points in FV.

11. Join all these points a, b, P3 and P4. It shows the cut portion of pyramid. Hatch that part.

Stage 2 – True Shape of Section

1. Draw the section line/plane on left side of TV (take the measurement from TV a to b).

2. Mark all points on section line using compass such as P3 and P4.

3. Take the projection of above points in FV, above XY line.

4. From sectional FV take the projections of a,b, P3 and P4 towards left side.

5. Mark the intersection points and join all these points.

6. True shape of section (TSS) a-b-P3-P4 will form. Hatch the TSS.

Stage 3 – Development

1. 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’4’. Say O1

2. Taking O1 as radius and O as centre draw an arc and divide it into 4 parts taking 35 mm as radius in compass (Development).

3. Joint all the points with apex O, O1, O2, O3, O4, O5, O6 and O1, six slant edges. Also join sides of bases 12, 23, 34, 45, 56 and 61

4. Take the projection of point P3’ and P4’ on line O1.

5. O as centre and OP3’ and OP4’as radius draw an arc, it will intersect slant edge O3. Mark that point P3 and P4 respectively.

6. Mark point a and b from TV on the development on side 2 3 and 4 5 respectively

7. Join a-b-P3-P4. Also draw other parts which is retained using continuous solid line .