## Development of lateral Surfaces of Two Intersecting Solids

### Sample Problem 1:A vertical square prism of side of base 45 mm and height 80 mm rests on HP with its faces equally inclined to VP. it is pierced centrally by a horizontal cylinder of 40 mm diameter and 80 mm length. Axis of the cylinder is parallel to VP and perpendicular to the axis of the prism. (1) draw the projections of the solids showing the curves of intersection. (2) Develop the lateral surfaces of the intersecting solids.  (UQ)

Steps for Development of lateral Surfaces of Two Intersecting Solids :

1. see Fig (i). Draw top, front and left side view of the vertical square prism.

2.Draw left side view of the horizontal cylinder. Project its front and top views.

3.Divide the cylinder circle in the left side view into 8 (or 12) equal parts.

4. Project the generators of the cylinder to its top and front views.

5. obtain the intersecting points in the top view at the points at which the generators of the cylinder intersect the rectangular faces of the square prism.

6. Project the intersection points from the top view to the front view.

7. Draw smooth curves of intersection in the front view as shown.

Development of lateral surfaces of Square Prism Vs Cylinder:

8. see Fig (ii). Draw vthe development of the lateral surfaces of the vertical square prism as a rectangle of size (4*45) mm * 80 mm.

9. divide the rectangle einto 4 equal parts.

10. Draw the curve of intersection in the above rectangle by transferring the distances from the corresponding top and left side views.

11. see Fig (iii). Draw a rectangle of size 40 Π mm * 80 mm to represent the development of the horizontal cylinder. Divide this rectangle into 8 (or 12 ) equal parts.

12. Draw the curve of intersection in the above rectangle by transferring the distances from the corresponding front view