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# Sections of Solids

### Sample Problem 1:A hexagonal prism, side of base 30 mm and axis 60 mm long, rests with its base on HP such that one of its rectangular faces is parallel to VP. A section plane perpendicular to HP and parallel to VP cuts the prism at a distance of 10 mm from its axis . Draw its top and sectional front views.

Steps for Section of Solids :

1. Draw top and front views of the prism by thin lines and name all the corners.

2.Draw SP parallel to XY and 10 mm from the axis towards the observer in the top view.

Note: Always major portion of the solid should be retained for projections.

3. Name the section points 1 & 2 where the S.P. cuts the visible edges ab and cd respectively. Name the points (3) and (4) where the S.P.  cuts the invisible edges (d1)(c1) and (b1)(a1) respectively. show remaining portion of prism as thick lines.

4. Cut surface: project the above section points on the corresponding edges  in the front view. From 1(4) draw a projector to cut a’b’ at 1′ and a1’b1′ at 4′. Similarly mark 2′ and 3′ in the front view.

join 1’2’3’4′ by thick lines and hatch this area to represent the front view of the cut surface.

5. Look at the remaining portion of the prism in the top view in the direction of arrows. 1a(a1)(4) and 2d (d1)(3) are visible. show 1’a’a1’4′ and 2’d’d1’3′ as thick lines.

### Sample Problem 2:A tetrahedron of 60 mm long edges rests with one of its faces on HP and an edge is perpendicular to VP. a section plane perpendicular to VP cuts the tetrahedron such that the true shape of section is an isosceles triangle of base 50 mm and altitude 36 mm.

Steps for Section of Solids :

Draw the front view,sectional top view and true shape of section.Also, find the inclination of the S.P. with HP.                 (UQ)

If the true shape of section is a triangle , the S.P. must cut 3 edges of the tetrahedron.

1.Obtain the true shape by projecting the cut surface on an A.I.P. parallel to S.P. For this, the  distances of section points in top view from XY are measured and transferred with reference to X1Y1.

For this, mark 1 and 3 on oa and oc respectively such that length 1-3 is equal to 50 mm(base of the triangle) and also perpendicular to XY.

2. project  1 and 3 on the corresponding edges in the front view.

3. 1′(3′) as center and 36 mm (altitude of Δ)  as radius draw an arc to cut o’b’ at 2′.

4. join 1′(3′) with 2′. Extend it to represent S.P. Angle θ between S.P. and XY is 42º.

5. project 2′ and mark 2 on ob. then complete sectional top view. Draw the shape of section , which is an isosceles triangle.