CONICS

1. Trace the curves when the distance of the focus from the directrix is 43 mm with eccentricity (a) 2/3 (b) 1 (c) 3/2. Name the curves. Draw normal and tangent at a distance of 50 mm from the focus.

2. The major and minor axes of an ellipse are 160 mm and 90 mm respectively. Find the foci and draw the ellipse by (a) concentric circles method (b) oblong method and (c) arcs of circles method. Draw a normal and tangent to the ellipse at a point 35 mm above the major axis.

3. Inscribe an ellipse in a rhombus of side 80 mm with the shortest diagonal of the rhombus being 80 mm. Use four centre method.

4. Conjugate axes of an ellipse are given as 130 mm and 80 mm respectively. They are inclined at 60o . Draw an ellipse and determine the major axis and minor axis. Also determine directrix and eccentricity.

5. Two points A and B are 150 mm apart. The point C is 100 mm from A and 60 mm from B. Draw an ellipse passing through A, B & C.

6. A ball thrown up in air reaches a maximum height of 70 mm and travels a horizontal distance of 100 mm. Trace the path of the ball assuming it to be parabolic. Find the direction of the ball at a height of 50 m from the ground. (Use rectangle method and 1:800 scale)

7. A bullet is discharged from the ground level at an inclination of 60o with the ground. The bullet reaches some height and returns to the ground at a horizontal distance 80 m. Trace the path of the bullet. Determine the height to which the bullet reaches. (Use tangent method and 1: 600 scale)

8. A stone is thrown from the top of a building 6 m high and across the top of a tree 12 m high and falls on the ground. The distance between the building and the tree is 4 m. Take a suitable scale and trace the path of stone till it reaches the ground.

9. Hyperbola is a curve traced out by a point P moving in such a way that the difference between its distances from two fixed points (Foci) is always constant and is 50 mm. The distance between the fixed points is 120 mm. Draw the curve.

10.Point A is 35 mm and 45 mm from two fixed straight lines which are at right angles to each other. Draw a rectangular hyperbola passing through A until the curve is 10 mm from the two straight lines.

CONICS AND CYCLOIDAL CURVES

1. A circle of 42 mm dia rolls along a straight line without slipping. Draw the curve traced out by a point on the circumference of the circle for one complete revolution of the circle. Draw the tangent and normal to the curve at a point on the curve 35 mm from the directing line.

2. A circle of 40 mm dia rolls along the floor for half a revolution and then on the wall for another half revolution. Draw the curve traced out by a point on the circumference of the circle.

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3. A circle of 40 mm dia rolls on the circumference of another circle 120 mm dia and outside it. Trace the locus of a point on the circumference of the rolling circle for one complete revolution. Name the curve. Draw a tangent and normal at a point on it 100 mm from the centre of the directing circle.

4. A circle of 40 mm dia rolls on another circle of 120 mm dia with internal contact. Draw the locus of a point on the circumference of the rolling circle for one complete revolution. Draw a normal and tangent to the curve at a point 30 mm from the centre of the directing circle.

5. Show by means of a drawing that when the dia of the directing circle is twice that of the rolling circle, the hypocycloid is a straight line. Take the dia of the generating circle as 50 mm.

INVOLUTES AND SPIRAL CURVES

1. Draw the involute of a circle of 36 mm dia. Draw a normal and a tangent to it at a point 100 mm from the centre of the circle.

2. Trace the path of a point P which is one end of a string when wound round a circle of 38 mm dia. The length of the string is 160 mm.

3. Draw the involute for a regular hexagon of 30 mm side. Draw tangent and normal to the involute at 154 mm away from the starting point.

4. A small stick of length equal to the circumference of a semicircle of 30 mm radius, initially tangential to the semi circle, rolls on the semi circle without slipping till it becomes tangential on the other side of the semi circle. Draw the loci of the end points of the stick. Name the curve.

5. Draw an Archimedean spiral of one and a half convolution, the greatest (max or highest) and the least (min or smallest) radii being 100 mm and 20 mm respectively. Draw a tangent and normal to the spiral at a point 80 mm from the pole.

6. An ant moves away from the pole and reaches a distance of 100 mm while the link on which the ant lies moves around the pole once. Its movement is uniform. Draw the curve traced by the ant.

7. A link 130 mm long swings at a point ‘O’ from its vertical position through an angle of 60o and returns to its initial position at uniform velocity. During that period an ant moves at a uniform speed from a distance of 20 mm from the point and reaches the end of the link. Draw the locus of the ant.

8. In the triangle ABC, AB = 20 mm, AC = 30 mm and CAB 60o. If B and C are the points on an Archimedean spiral of one convolution and A is the pole, find the initial line and draw the spiral.

9. Draw for one convolution of an Archimedean spiral represented by the polar equation r = 12+14, where ‘r’ is in mm and ‘’ is in radian measure. Draw a tangent and normal to the curve at a point 75 mm from the pole.

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PROJECTIONS OF POINTS

1. Draw the projections of the following points on the same reference line(xy line), keeping the projectors 25 mm apart :

A. in the H.P. and 25 mm behind the V.P.

B. 40 mm above the H.P. and 25 mm in front of the V.P.

C. in the V.P. and 40 mm above the H.P.

D. 25 mm below the H.P. and 25 mm behind the V.P.

E. 15 mm above the H.P. and 50 mm behind the V.P.

F. 40 mm below the H.P. and 25 mm in front of the V.P.

G. in both the H.P. and the V.P.

2. Projections of various points are given in the Figure. State the position of each of the points with respect to the planes of projection, giving the distances in mm.

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PROJECTIONS OF STRAIGHT LINES – I

1. Draw the projections of an 80 mm long line in the following positions.

A. (i) parallel to both H.P. and V.P. : 30 mm above H.P. and 20 mm in front of V.P.

(ii) parallel to 35 mm above H.P. and in V.P.

(iii) parallel to and 45 mm in front of V.P. and in H.P.

B. (i) perpendicular to H.P. 30 mm in front of V.P. and its one end 20 mm above H.P.

(ii) perpendicular to V.P. 20 mm above H.P. and its one end in V.P.

(iii) perpendicular to H.P. in V.P. and its one end in H.P.

C. (i) inclined at 30o to V.P. in H.P and its one end in V.P.

(ii) inclined at 40o to H.P., its one end 25 mm above it parallel to and 30 mm in front of V.P.

(iii) inclined at 40o to V.P. and its one end 10 mm in front of it, parallel to and 20 mm above H.P.

2. A 90 mm long line is parallel to and 30 mm above H.P. Its two ends are 20 mm and 40 mm in front of V.P. respectively. Draw its projections and find its inclination with V.P.

3. A 85 mm long line is parallel to and 20 mm in front of V.P. Its one end is in the H.P. while the other is 45 mm above H.P. Draw its projections and find its inclination with H.P.

4. The top view of an 80 mm long line measures 50 mm. The line is in V.P, its one end being 20 mm above H.P. Draw its projections.

5. The front view of a line inclined a 35o to V.P is 60 mm long. Draw the projections of the line when it is parallel to and 45 mm above H.P. its one end being 25 mm in front of V.P.

6. Two pegs fixed on a wall are 5 m apart. The distance between the pegs measured parallel to the floor is 3.5 m. if one peg is 1 m above the floor, find the height of the second peg and inclination of the line joining the two pegs with the floor. (Use 1 : 50 scale0

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PROJECTIONS OF STRAIGHT LINES – II

1. A line AB 100 mm long is inclined at 40o to H.P. and 35 o to V.P. Its one end is 15 mm above H.P. and 20 mm in front of V.P. Draw its projections and determine its traces.

2. A line PQ 70 mm long has its end P 15 mm above H.P and 30 mm in front of V.P. The end Q is 45 mm above H.P. and 70 mm in front of V.P. Draw its projections and determine its inclinations with H.P. and V.P. and its traces.

3. The length of the top view of a straight line AB is 70 mm and front view is 65 mm. The front view is inclined at 30o to xy line. Draw the projections of the line assuming the point A to be 10 mm above H.P. and 30 mm in front of V.P. Determine its traces, check the problem with trapezoidal method.

4. Two oranges on a tree are respectively 2m and 4 m above the ground and 1 m and 2 m from a 0.2 m wall on opposite sides of it. The distance between the oranges measured above the ground parallel to the wall is 3 m. Determine the true distance between them (use 1 : 50 scale).

5. The top view of a line is 70 mm long, and inclined at 35o to xy line. Its one end is 15 mm above H.P. and 20 mm in front of V.P. Determine true length of the line and its true inclinations, if the other end is 60 mm above H.P.

6. The end A of a line AB is in H.P and 30 mm in front of V.P. The end B is in V.P. and 60 mm above H.P. The distance between the end projectors is 80 mm. Draw the projections of the line, determine true length, true inclinations and traces.

7. Draw the projections of a line AB 100 mm long, its mid point M being 50 mm above H.P. and 45 mm in front of V.P. Its one end is 30 mm above H.P. and 15 mm in front of V.P. Show its traces and true inclinations with H.P. and V.P.

8. The projections of a line measure 90 mm in the top view and 80 mm in the front view. The mid point of the line is 40 mm in front of V.P. and 50 mm above H.P. One end is 15 mm in front of V.P. and nearer to it. The other end is nearer to H.P. Draw the projections of the line, determine its true length and true inclinations.

9. The projectors from the H.T and V.T. of a straight line AB are 90 mm apart, while those drawn from its ends are 60 mm apart. The H.T. is 30 mm in front of V.P. and V.T. is 60 mm above H.P. Its one end A is 15 mm above H.P. Draw the projections of the line and determine its true length and inclinations with H.P. and V.P.

10.The end of A of a line AB is 25 mm above H.P. and 15 mm in front of V.P. and B is 50 mm above H.P. and 30 mm in front of V.P. The distance between end projectors is 50 mm. Draw the projections of the line, determine true inclinations and traces. (check the problem using trapezoidal method).

11.The line AB is inclined at 40o to V.P. and has its ends 30 mm and 50 mm above the H.P. respectively. The length of the front view is 65 mm and its V.T. is 12 mm above H.P. Determine its true length, true inclination with H.P. and H.T.

12.A line AB has its end A 20 mm and end B 50 mm in front of V.P. respectively. The distance between the end projectors is 70 mm. The line is inclined at 35o

to H.P and its H.T. is 15 mm above xy line. Draw the projections of AB and determine its true length and inclination with V.P. and its V.T.

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13.A room is 6 m long, 4 m wide and 3 m high. An electric lamp is suspended from the center of the ceiling and at a distance of 1 m from it. Find the distance of the lamp from one corner of the floor.

14.A divider opened to an angle of 40o has its ends 30 mm apart and rests on H.P., such that the ends are at a distance of 15 mm and 40 mm in front of V.P. The hinged point is 30 mm above H.P. Draw the projections and find the true lengths of the legs.

15.Draw an isosceles triangle ABC of base AB 40 mm and altitude 75 mm with a on xy line and ab inclined at 45o to xy line. The figure is top view of a triangle ABC whose corners are 75 mm, 25 mm and 50 mm above H.P. respectively. Determine the true shape of the triangle and inclination of the side AB with the two planes of projection.

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PROJECTIONS OF PLANES

1. An equilateral triangle of side 55 mm has its plane parallel to V.P. and 40 mm in front of it. Draw its projections when one of its sides is (a) perpendicular to H.P. (b) parallel to H.P. (c) inclined at 40o to H.P. Find its traces.

2. A pentagonal lamina of 25 mm side has one side in H.P. Its plane is inclined at 50o to H.P. Draw its projections and determine its traces.

3. A square lamina of side 60 mm has a corner in V.P. Its plane is inclined at 40o

to V.P. Draw its projections and determine its traces.

4. A regular pentagon of side 40 mm has a corner in H.P. Its surface is inclined at 50o to H.P. and the top view of the line passing through the centre and the corner makes an angle of 30o with xy line. Draw its projections.

5. A regular hexagon of 30 mm side has an edge in the H.P. Its surface is inclined at 30o to H.P. and the edge on which it rests makes an angle of 40o

with V.P. Draw its projections.

6. A regular hexagon of 35 mm side has a corner in the V.P. Its surfaces is inclined at 45o to V.P. and the diagonal passing through the corner makes an angle of 35o with the H.P. Draw its projections.

7. A regular pentagon of 40 mm side has an edge in V.P. Its surface is inclined at 45o to V.P. and the edge on which its rests makes an angle of 35o with H.P. Draw its projections.

8. A circular lamina of 60 mm diameter rests on V.P. such that the surface of the lamina is inclined at 40o to V.P. Draw its projections when (a) the diameter passing through the point on which it rests makes an angle of 40o with H.P. (b) the top view of the diameter passing through the point on which it rests makes an angle of 40o with H.P.

9. Draw the projections of a rhombus having diagonals 100 mm and 50 mm long, the smaller diagonal of which is parallel to both the planes, while the other is inclined at 50o to H.P.

10.A rhombus of diagonals AC = 110 mm and BD = 60 mm has the corner A in H.P. and the plane is inclined to H.P. such that the top view appears as a square. The top view of the diagonal passing through A makes an angle of 30o

to V.P. Draw the projections and find the inclination of the plane with H.P.

11.A 30o – 60O set square has its shortest side 60 mm in H.P. The top view of the set square is an isosceles triangle and the longer edge is inclined at 40o with V.P. Draw the projections of the set square and find its inclination with H.P.

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PROJECTIONS ON AUXILIARY PLANES

1. The lengths of the front view and top view of a straight line AB are 60 mm and 50 mm respectively. The distance between end projectors is 40 mm and one end A is 20 mm above H.P. and 30 mm in front of V.P. Determine the true length of the line AB and inclinations using auxiliary plane method.

2. The end A of a line AB is 15 mm above H.P. and 20 mm in front of V.P The top view makes an angle of 40o with xy line. Draw its projections. Determine the shortest distance of the line from the reference line and also distance of mid point from the reference line.

3. The point P of a line PQ is 80 mm in front of V.P. and 30 mm above H.P., whereas Q is 20 mm in front of V.P. and 75 mm above H.P. The projections of the line lie on the same projector. Draw the projections and determine its true length and true inclinations with H.P. and V.P.

4. A regular pentagon has a side of 40 mm parallel to H.P. The side is inclined at an angle of 40o with V.P. Its surfaces is inclined at an angle of 30o with H.P. Draw its projections.

5. A regular hexagon of 30 mm side has a corner in V.P. The diagonal passing through the corner makes an angle of 35o with H.P. Its surface is inclined at 40o with V.P. Draw the projections.

6. A regular pentagonal plane ABCDE of side 50 mm is resting on the side AB in V.P. Its plane makes an angle of 40o with V.P. Draw the projections of the plane when the front view of the line joining the mid point of AB and the centroid O makes an angle of 40o with H.P.

7. A hexagonal plate of 30 mm side has one corner touching V.P. and the opposite corner touching H.P. The plane is inclined at 60o with V.P. and 30o

with H.P. Draw the projections of the plate.

8. A circle of 60 mm diameter has the end A of diameter AB in H.P. The top view of the diameter AB makes an angle of 30o with xy line. Its surface is inclined at 60o to H.P. Draw the projections.

9. An isosceles triangle ABC, base 60 mm and altitude 40 mm has its base AC in H.P. and inclined at 40o to V.P. The corners A and B are V.P. Draw its projections.

10.Determine the true shape of the figure, the top view of which is a regular pentagon of 35 mm side having one side inclined at 45o to xy line and whose front view is straight line making an angle of 50o with xy line.

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PROJECTIONS OF SOLIDS

1. Draw the projections of the following solids situated in the respective positions taking the side of the base equal to 35 mm axis 75 mm.

a. A triangular prism, base in V.P. a side of the base inclined at 35 to H.P.

b. A square prism, base in H.P. a side of the base perpendicular to V.P.

c. A pentagonal prism, rectangular face in V.P. and axis perpendicular to H.P. with one base in H.P.

d. A hexagonal prism, base in V.P. and side of the base parallel to and 30 mm above H.P.

e. A triangular pyramid, base in H.P. a side of base inclined at 30o to V.P.

f. A square pyramid, base in V.P. all sides of base equally inclined to H.P.

g. A pentagonal pyramid, base on H.P. and a side of a side of base perpendicular to V.P. and axis 50 mm in front of V.P.

h. A hexagonal pyramid, base in V.P. and a side of base perpendicular to H.P.

2. Draw the projections of the following solids situated in their respective positions taking the side of the base equal to 35 mm and axis 75 mm.

a. A cylinder, axis perpendicular to H.P. and 50 mm in front of V.P. and one end 25 mm above H.P.

b. A cylinder, axis perpendicular to V.P. and 40 mm above H.P. and one end in V.P.

c. A cone, apex in V.P. axis perpendicular to V.P. and 50 mm above H.P.

d. A cone, resting on H.P. on its base and its axis 60 mm in front of V.P.

3. Draw the projections of a tetrahedron of side 75 mm when it is resting in V.P. on one of its faces with the edge of the face inclined at 40o to H.P.

4. A cube of 40 mm side has one face in H.P. and adjacent face is inclined at 30o

to V.P. Its one edge of the lateral face is touching V.P. Draw the projections.

5. A square pyramid of base of side 35 mm and height 60 mm is resting on H.P. on its base with all edges of the base equally inclined to V.P. Draw its projections.

6. A hexagonal prism of side of base 30 mm and height 70 mm is resting on H.P. with the axis perpendicular to V.P. Draw the projections.

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SECTIONS OF SOLIDS

1. A cube of side 60 mm is resting on H.P. on one of its faces with one of the vertical faces inclined at 40o to V.P. It is cut by a section plane perpendicular to V.P. and inclined at 40o to H.P. passing through a point 40 mm on the axis above the H.P. Draw the projections of sectioned solid and true shape of the section.

2. A cube of side 50 mm is cut by a sectional plane such that the true shape is a regular hexagon. Draw the projections of the sectioned solid and find the inclination of the sectional plane with the H.P.

3. A hexagonal prism of base of side 30 mm and 70 mm long has a rectangular face in H.P. and axis parallel to V.P. It is cut by a plane perpendicular to H.P. and inclined at 40o to V.P. and passing through a point on the axis 40 mm from one of its ends. Draw the projections and determine the true shape.

4. A tetrahedron of 50 mm side is lying in H.P. on one of its faces with one of the sides inclined at 30o to V.P. It is cut by a section plane perpendicular to V.P. and inclined to H.P. such that the true shape of the section is an isosceles triangle of base 30 mm and altitude 35 mm. Draw the front view, sectional top view and determine the true shape.

5. A square pyramid of 60 mm side and 80 mm axis is resting on its base on ground with one of the edges of the base perpendicular to V.P. It is cut by an inclined plane in such a way that the true shape of the section is a trapezium whose parallel sides measures 46 mm and 26 mm. Draw the sectional views and true shape of the section. Determine the inclination of the sectional plane with H.P.

6. A pentagonal pyramid of side of base 30 mm and axis 70 mm long rests with its base on H.P. with the edge of the base inclined at 30o to V.P. It is cut by a section plane perpendicular to V.P. and inclined at 45o to H.P. and passing through a point 35 mm from base. Draw the projections and determine the true shape.

7. A cylinder of 50 mm dia of base and 80 mm height is lying on H.P. on one of its generators and has its axis parallel to H.P and inclined at 40o to V.P. It is cut by a section plane perpendicular to H.P. and inclined to V.P in such a way that the true shape of the section is an ellipse having the major axis 60 mm long. Draw the projections of the solid and the true shape of the section.

8. A cone of base of 50 mm and 75 mm rests with its base on H.P. It is cut by a section plane parallel to one of the generators and 12 mm away from it. Draw the sectional top view and true shape of the section.

9. A cone of base of 40 mm dia and 70 mm height rests with its base on H.P. It is cut by an inclined plane intersecting the axis such that the true shape is an ellipse of major axis 30 mm. Draw the projections.

10.A triangular prism of base 30 mm side and axis 50 mm long is lying on the ground on one of its rectangular faces with its axis inclined at 30o to V.P. It is cut by a horizontal section plane at a distance of 12 mm above the ground. Draw its front view and sectional top view.

11.A right circular cone (base dia 40 mm) and height 60 mm rests on its base in H.P. It is cut by (i) an inclined plane making 35o with H.P. and passing through the axis at 35 mm below apex. (ii) An AVP making 25o with V.P. and 5 mm away from the center of the base. Draw the front view and top view of the cut section also draw true shape of the cut portion of the solid.

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DEVELOPMENT OF SURFACES

1. A cube of 50 mm side with its square faces equally inclined to V.P. and resting on H.P. is cut by a section plane perpendicular to V.P. and inclined at 50o to H.P. and passing through the mid point of the axis. Develop the lateral surface of the lower portion of the solid.

2. A pentagonal prism 30 mm side of base is resting on H.P. with side of the base perpendicular to V.P. The VT of the cutting plane is inclined at 30o to the axis of the prism and passes through the right corner of the top base in front view. Develop the lower portion of the solid.

3. A hexagonal prism of 25mm side of base 60mm height is resting on H.P. such that two rectangular faces are perpendicular to V.P. A circular hole of 28mm dia is drilled through the prism such that the axis of the hole bisects the axis of the prism at right angles and perpendicular to V.P. Draw the development showing the hole also.

4. A vertical cylinder of 50mm dia of base and 70mm long is resting on H.P. A circular hole of 40 dia is drilled through the cylinder with an offset of 15 mm from the axis of the cylinder in the front view at the central plane perpendicular to V.P. Develop the lateral face of the cylinder showing the shape of the hole on it.

5. A hexagonal pyramid of side of base 25mm and height 65mm rests vertically with two of its base edges equally inclined with V.P. A cutting plane perpendicular to V.P. cuts the axis at 35mm from the base and inclined at 35o

to H.P. Draw the development of the lateral face of the lower portion of the solid.

6. A cone of 60mm dia of base and 75 mm height is on H.P. and is cut by a section plane perpendicular to V.P. bisecting the axis and inclined at 50o to the axis. Draw the development of the lateral portion of the cone.

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INTERSECTION OF SURFACES

1. A square prism of 40 mm side and height 70 mm stands with its base on H.P. with two of its rectangular faces equally inclined to V.P. A horizontal square prism of side of base 30 mm and 80 mm long penetrates the vertical prism such that the axes bisect each other at right angles and the horizontal prism has its axis parallel to V.P. Two of the rectangular faces of the horizontal prism are equally inclined to H.P. Draw the projections showing the lines of intersection.

2. A vertical square prism base of 40 mm and height 70 mm is resting on H.P. with two of its rectangular faces equally inclined to V.P. It is completely penetrated by a horizontal square prism of side 30 mm and axis 70 mm long so that their axes are 5 mm apart. The axis of the horizontal prism is parallel to H.P. while its faces are equally inclined to H.P. Draw the projections of the prism showing the lines of intersection.

3. A vertical cylinder of 50 mm dia. and 70 mm length is penetrated by a horizontal cylinder of 30 mm diameter and 70 mm length such that their axes bisect each other at right angles. Assume that the axis of the horizontal cylinder is parallel to both the planes. Draw the curves. Assume that the vertical cylinder rests on H.P.

4. A vertical cylinder of 50 mm diameter and 80 mm long is penetrated by a horizontal cylinder of 50 mm dia. and 80 mm length. The axis of the horizontal cylinder is 5 mm away from the axis of the vertical cylinder. Draw the intersection curves assuming that the axis of the horizontal cylinder is parallel to both H.P and V.P.

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ISOMETRIC PROJECTIONS

1. Draw the isometric projection of a rectangle of size 60 mm x 30 mm if the surface is

a. Vertical b. Horizontal

2. Draw the isometric projection of a regular pentagon of 20 mm side if the surface is

a. Vertical b. Horizontal

3. Draw the isometric view of a circle of 40 mm diameter if the surface is

a. Vertical b. Horizontal

4. Draw the isometric view of the hexagonal prism, side of base 20 mm and axis 50 mm long, when its axis is vertical. Assume that two of the rectangular faces are equally inclined to V.P.

5. Draw the isometric view of a pentagonal pyramid of 25 mm side of base and 60 mm height, which rests with its base on H.P. and a base edge parallel to V.P.

6. A frustum of a cone of 20 mm top diameter and 50 mm bottom diameter and axis length 30 mm is placed vertically on a cylinder of 60 mm diameter and 20 mm height such that both the solids have a common axis. Draw the isometric view of the combination of the solids.

7. Fig. 17.71 (N.D.Bhatt)

8. Fig. 17.82 (N.D.Bhatt)

9. Fig. 17.85 (N.D.Bhatt)

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ISOMETRIC PROJECTIONS

1. Draw the isometric views of the following solids whose axis is perpendicular to the HP.

a. Hexagonal prism- base side 20 mm, axis 60 mm

b. Pentagonal pyramid – base side 30 mm, axis 70 mm

c. Cylinder base 40 mm diameter, axis 60 mm long

d. Cone base 50 mm diameter, axis 75 mm long

e. Frustum of a square pyramid bottom base 50 mm side, top base 30 mm side, axis 60 mm long.

f. Frustum of a cone bottom base 40 mm diameter, top base 20 mm diameter, height 60 mm long

2. Draw the isometric projection of the following solids whose axis is perpendicular to the V.P.

a. Pentagonal prism base side 30 mm, axis 60 mm long

b. Hexagonal pyramid base side 20 mm, axis 60 mm long

c. Cylinder base 50 mm diameter, axis 70 mm long

d. Cone base 40 mm diameter, axis 60 mm long

3. A sphere of 40 mm diameter is resting centrally on the top base of a frustum of a cone of bottom base 50 mm diameter and top base 30 mm diameter, height 70 mm which is resting vertically.

4. A frustum of a cone of bottom base 40 mm diameter, top base 20 mm is placed at the centre of a top base of a hexagonal prism of base side 25 mm and axis 70 mm long, so that the axes of both the solids are coinciding and is vertical.

5. A frustum of a cone of 20 mm top diameter and 50 mm bottom diameter and axis length 30 mm is placed vertically on a cylinder of 60 mm diameter and 20 mm height such that both the solids have a common axis. Draw the isometric view of the combination of the solids.

6. Draw the isometric view of the solids whose orthographic views are as given in figures

7. Fig. 17.45 (N.D.Bhatt – Page. 406)

8. Fig. 17.80 (N.D.Bhatt – Page.414)

9. Fig. 17.90 (N.D.Bhatt)

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