Development of surfaces Exercise

Parallel Line Development Method Draw the development of the lateral surface of a right square prism of edge of base 30 mm and axis 50 mm long.

STEPS: Draw the top and front view of the prism and name the corners. It consists of four equal rectangles of size 50 mm X 30 mm in contact and in sequence. Hence draw the rectangle A1A1AA such that A1A1 = perimeter of the base of the base of the prism and AA1 = its height 3. On the line A1A1, mark four equal divisions A1B1,B1C1, etc., each equal to the side of base 30 mm. 4. Erect perpendiculars at B1,C1, and D1. Darken the four rectangles which give the development of the lateral surface of the prism.

SOLUTION

Prob2: Draw the development of the outside case and tray of a match-box of size 45 mm X 33 mm X 16 mm.

Prob3: Draw the development of the complete surface of a G.I. cylindrical drum with lid. Diameter is 30 cm and the height is 1.6 times the diameter.

Prob4: Develop the complete surface of a cube of 35mm side.

Prob5: Develop the lateral surface of a pentagonal prism of side of base 25 mm and height 50 mm.

Prob6: A hexagonal prism, edge of base 20mm and axis 50 mm long, rests with its base on H.P. Such that one of its rectangular faces is parallel to V.P. it is cut by a plane perpendicular to V.P., inclined at 450 to H.P and passing through the right corner of the top face of the prism. Draw the sectional top view and develop the lateral surface of the truncated prism.

Prob6:

Prob7: A vertical chimney of 70 cm diameter joins a roof sloping at an angle of 350 with the horizontal. The shortest portion over the roof is 32cm. Determine the shape of the sheet metal from which chimney can be fabricated.

Radial – line development Exercise

Prob 8 Draw the development of the lateral surface of a square pyramid, side of base 25 mm and height 50 mm, resting with its base on H.P. and an edge of the base parallel to V.P.

Answer

Prob 9 A pentagonal pyramid , side of base 30 mm and height 52 mm, stands with its base on H.P. and an edge of the base is parallel to V.P. it is cut by a plane perpendicular to V.P., inclined at 400 to H.P. and passing through a point on the axis, 32 mm above the base. Draw the sectional top view and develop the lateral surface of the truncated pyramid.

Prob 10 A cone of base 50 mm diameter and height 65mm rests with its base on H.P. A section plane perpendicular to V.P. and inclined at 300 to H.P. bisects the axis of the cone. Draw the development of the lateral surface of the truncated cone.

Prob 11 A lamp shade is formed by cutting cone of base 144 mm diameter and 174 mm height by a horizontal plane at a distance of 72 mm from the apex and another plane inclined at 300 to H.P., passing through one extremity of the base. Draw the development of the shade.

Prob 12 A cone of base 50 mm diameter and 60 mm height, rests with its base on H.P. it is cut by a section plane perpendicular to V.P., parallel to one of the generators and passing through a point on the axis at a distance of 22 mm from the apex. Draw the sectional top view and develop the lateral surface of the remaining portion of the cone.

Intersection of surfaces Next Class Intersection of surfaces