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# Intersection of Surfaces

### Sample Problem 1: The front view of a cone resting on its base on HP is an equilateral triangle of 75 mm side with one side horizontal. It is penetrated by a square prism of side 25 mm. The rectangular faces of the prism are equally inclined to HP. The axis of the prism is perpendicular to VP and meets that of the cone 25 mm above the base. Draw the three views of the cone showing the curves of intersection.

Steps for Intersection of Surfaces:

1. Draw the front view of the cones an equilateral triangle. project the top and side views of the cone.

2.In the front view, draw the front view of the square prism as a square equally inclined to XY at a height of 25 mm from the base.

3.Assume the solids to be cut by different section planes in the region of the prism.Accordingly, mark the section plane as 1’1′,2’2′ ,3’3′ , etc., in the front view.

4. mark a’ at the point of intersection of the S.P.  1’1′ with the surface of the prism.

5. mark b’ and b’ at the points of intersection of the S.P. 2’2′ with the surfaces of the prism.

6. Similarly mark c’ & c’, d’ & d’ and e’.

7. with o (the apex in the top view) as center  and 1’1′ as diameter ,draw circle cutting the projector through a’ at a.

8. similarly mark b,c,d and e. join the projected points in the top view in proper sequence by a smooth curve. then complete the top view, assuming suitable length of the prism.

9. the method of locating the points a” & a” in the side view is clearly shown by mitre line. Thus complete the side view as shown.