A lamp shade is formed by cutting a cone of base 144 mm diameter and 174 mm height by a horizontal plane at a distance of 72 mm from the apex and by an another plane inclined at $30^{\circ}$ to HP and passing through one extremity of the base. Draw the development of the lampshade. (Answer any two full question. Each question carries 17 marks)

Explanation

The development of the lampshade is drawn by first drawing the top view of the cone on the auxiliary plane. The top view of the cone is cut by a horizontal plane at a distance of 72 mm from the apex. The horizontal plane intersects the cone at a circle. The development of the lampshade is drawn by projecting the top view of the cone on the auxiliary plane. The development of the lampshade is a trapezium with the top view of the cone as its base. The development of the lampshade is drawn by using the auxiliary projection formula: $x = x' \tan \phi$ and $y = y' \tan \phi$. The development of the lampshade is drawn by using a set square and a ruler. The development of the lampshade is drawn by using a ruler and a compass.

Explanation

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