Vtu problems projection of plane surfaces

SOLUTIONS TO

VTU QUESTIONS

PROJECTION OF PLANE SURFACES

PREPARED BY

PRUTHVI LOY SERRAOGOPAL KRISHNA BALIGA

SELECT QUESTION

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21 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 50

1. An Equilateral triangular lamina of 25mm side lies with one of its edges on HP such that the surface of the lamina is inclined to HP at 60°. The edge on which it rests is inclined to VP at 60 °. Draw the projections.

PROJECTION OF PLANE SURFACES

X YVPHP

a

b

c

25

c'(a') b' c'(a')

b'

a

b

c

ab

c

a'

b'

c'60°

60°

PRUTHVI LOY SERRAO

2. An Equilateral triangular lamina of 25mm side lies with one of its sides on HP. The lamina makes 45° with HP and one of its medians is inclined at 40° to VP. Draw its projections.

X YVPHP

a

b

c

25

c'(a') b' c'(a')

b'

a

b

c a

bc

a'

b'

c'45°40°

d2d1

d1d2

β

locus of D

PROJECTION OF PLANE SURFACES PRUTHVI LOY SERRAO

3. A triangular lamina of 25mm sides rests on one of its corners on VP such that the median passing through the corner on which it rests is inclined at 30° to HP and 45° to VP. Draw its projections.

X YVPHP

a'

a

c'

25

b(c)

b'

a a

b c

a'

b'

c'

45°α

d1'locus of D


a'

c'

b'

d2'

b(c)

30°

d1'd2'

4. A triangular lamina of 25mm sides rests on one of its corners on HP such that the surface of the lamina makes an angle of 60° with HP. If the side opposite to the corner on which the lamina rests makes an angle of 30° with VP. Draw its projections.

X YVPHP


a

c25

b

a

b

c'(b')a' 60°

c

c'(b')

a'30°

a'

b' c'

a

b

c

5. A triangular lamina of 25mm sides rests on HP with one of its corners touching it, such that the side opposite to the corner on which it rests is 15mm above HP and makes an angle of 30° with VP. Draw its projections. Also determine the inclination of the lamina with the reference plane.


X YVPHP

a

c25

b

a

b

c'(b')a'

c

c'(b')

a'30°

a'

b' c'

a

b

c

15θ

Ans: Lamina Inclination = 44°

6. A 30°-60° setsquare of 60mm longest side is so kept such that the longest side is in HP, making an angle of 30° with VP. The setsquare itself is inclined at 45° to HP. Draw the projections of the setsquare.

X YVPHP

60 30°


60°

45°

a

b

c

a

b

c

a b

c

c'(a') b' c'(a')

b'

a'

b'

c'30°

7. An isosceles triangular plate of negligible thickness has base 25mm long & altitude 35mm. It is so placed on HP such that in the front view it is seen as an equilateral triangle of 25mm sides with the side that is parallel to VP is inclined at 45 ° to HP. Draw its top and front views. Also determine the inclination of the plate with the reference plane.

X YVPHP

2545°


3525

ɸ

a'

c'

b'

a(c) b

a'

c'b'

a(c)

b

a'

c'b'

a

b

c

Ans: Lamina Inclination = 52°

8. A square lamina of 40mm side rests on one of its sides on HP. The lamina makes 30° to HP and the side on which it rests makes 45° to VP. Draw its projections.

X YVPHP

40

30°


b'

b45°

a

cd

ba

cd

b

a

c

d

d'(a') c'(b') d‘(a')

c'(b')

d'

c'

a'

9. A square plate of 30mm sides rests on HP such that one of the diagonals is inclined at 30° to HP and 45° to VP. Draw its projections.

X YVPHP

40

30°


a'

b 45°

β

ca

d

b

ca

d

b c

ad

c'd'(b') a'

c'(b')d'

a'

b'

c'

d'

Locus of A

10. A square lamina ABCD of 40mm side rests on corner C such that the diagonal AC appears to be at 45° to VP. The two sides BC and CD containing the corner C make equal inclinations with HP. The surface of the lamina makes 30° with HP. Draw its top and front views.


XVPHP

40

30°a'

b

ca

d

b

ca

d

c'd'(b')

a'

c'

(b')d'

45°

b c

ad

a'

c'

b'd'

11. The top view of a square lamina of side 30mm is a rectangle of sides 30mm x 20mm with the longer side of the rectangle being parallel to both HP and VP. Draw the top and front views of the square lamina. What is the inclination of the surface of the lamina with HP and VP?


X YVPHP

30

θ

b 45°a

cd

ba

cd

d'(a') c'(b') d‘(a')

c'(b')

48°

42°

b

a

c

d

a'd'

b'c'

d"(a")

c"(b")X1

Y120

RPP

Ans: Lamina Inclination : HP = 48° & VP = 42°

12. A rectangular lamina of sides 20mm x 30mm rests on HP on one of its longer edges. The lamina is tilted about the edge on which it rests till its plane surface is inclined to HP at 45°. The edge on which it rests is inclined at 30° to VP. Draw the projections of the lamina.


X YVPHP

30

45°

ba

cd

ba

cd

d'(a') c'(b') d'(a')

c'(b')

20

30°

b

a

c

d

a'

c' b'

d'

13. A rectangular lamina of 35mm x 20mm rests on HP on one of its shorter edges. The lamina is rotated about the edge on which it rests till it appears as a square in the top view. The edge on which the lamina rests being parallel to both HP & VP. Draw its projections and find its inclinations to HP & VP.

X YVPHP


45°

55°

35°

d"(a")

c"(b")

X1

Y1

RPP

20

ba

cd

ba

cd35

θ

b

a

c

d

d'(a') c'(b') d'(a')

c'(b')

a'

c' b'

d'


20

14. A rectangular lamina of 35mm x 20mm rests on HP on one of its shorter edges. The lamina is rotated about the edge on which it rests till it appears as a square in the top view. The edge on which the lamina rests is inclined at 30° to VP. Draw its projections & find its inclinations to HP.

X YVPHP


20

ba

cd

ba

cd

θd'(a') c'(b') d'(a')

c'(b')

35

30°

b

a

c

d

a'

c' b'

d'

Ans: Lamina Inclination = 55° to HP

20

15. A rectangular lamina of sides 20mm x 25mm has an edge in HP and adjoining edge in VP. It is tilted such that the front view appears as a rectangle of 20mm x 15mm. The edge which is in VP is 30mm from RPP. Draw the top, front and left profile views in this position and find its inclinations with the corresponding principal planes.

X YVPHP


45°

X1

Y1

ɸ

20

25 15

30

b(a)a'

c'b'

d' a'

c'b'

d' a"

c"b"

d"c(d) b(a)

c(d)

RPP

(LSV)

Ans: Lamina Inclination = 53° to VP

16. The front view of a rectangular lamina of sides 30mm x 20mm is a square of 20mm sides. Draw the projections and determine the inclinations of the lamina with HP and VP.

X YVPHP


a(d)

20

b'

c'd'

b'a'

c'd'

30

b

a

c

d

a'

20

b(c) a(d)

b(c)

b'

a'

c'

d'

45°

42°

48°

a" (d")

b"(c")

X1

Y1

RPP

ɸ


17. A mirror 30mm x 40mm is inclined to the wall such that its front view is a square of 30mm side. The longer sides of the mirror appear perpendicular to both HP and VP. Draw the projections and find the inclinations of the mirror with the wall.


X YVPHP a(d)

30

b'

c'd'

b'a'

c'd'

40

b

a

c

d

a'

30

b(c) a(d)

b(c)

b'

a'

c'

d'

45°

49°

41°

a"(d")

b"(c")

X1

Y1

RPP

ɸ


18. A rectangular plate of negligible thickness of size 35mm x 20mm has one of its shorter edges in VP with that edge inclined at 40° to HP. Draw the top view if its front view is a square of side 20mm.

X YVPHP


20

35

b'

c'd'

a' b'a'

c'd'

20

a(d)

b(c)

ɸa(d) b(c)

b'

a'c'

d'

b

a

c

d 40°

Ans: Lamina Inclination : VP = 55°

19. A pentagonal lamina of edges 25mm is resting on HP with one of its sides such that the surface makes an angle of 60° with HP. The edge on which it rests is inclined at 45° to VP. Draw its projections.

X YVPHP


25

ba

c

d

e'(a') d'(b')

e

c' e'(a')

d'(b')

c'

ba

c

de

60°

45°

ba

c

d

e

a'

b'

c'

d'

e'

20. A pentagonal lamina of edges 25mm is resting on HP with one of its corners such that the plane surface makes an angle of 60° with HP. The two of the edges containing the corner on which the lamina rests make equal inclinations with HP. When the edge opposite to this corner make an angle of 45° with VP and nearer to the observer, draw the top and front views of the lamina in this position.


X YVPHP

bc

d

e'(b') d'(c')

e

a'

b

a

c

d

e

e'(b')

d'(c')

a'

25

a

60°

45°b

ac

de

a'

b'

c'd'

e'

21. A pentagonal lamina of edges 25mm is resting on HP with one of its corners such that the edge opposite to this corner is 20mm above HP & makes an angle of 45° with VP. Draw the top & front views of the plane lamina in this position. Determine the inclination of the lamina with HP.


X YVPHP

bc

d

e'(b') d'(c')

e

a'

b

a

c

de

e'(b')

d'(c')

a'

25

a

20θ

45°

b

a

c

d

e

a'

b'

c' d'

e'

Ans: Lamina Inclination : HP = 31°

22. A pentagonal lamina of sides 25mm is resting on one of its edges on HP with the corner opposite to that edge touching VP. This edge is parallel to VP and the corner, which touches VP is at a height of 15mm above HP. Draw the projections of the lamina and determine the inclinations of the lamina with HP and VP and the distance at which the parallel edge lies VP.


X YVPHP

25

ba

c

d

e'(a') d'(b')

e

c' e'(a')d'(b')

c'

ba

c

de

θ θφ

45°b

a

cd

e

a'

b'c'

d'

e'

c"b"(d")

a"(e")

X1

Y1

RPP


15

D

Distance of parallel edge from VP = 35.43

23. A pentagonal lamina having edges 25mm is placed on one of its corners on HP such that the perpendicular bisector of the edge passing through the corner on which the lamina rests is inclined at 30° to HP and 45° to VP. Draw the top and front views of the lamina.


X YVPHP

bc

d

e'(b') d'(c')

e

a'

b

a

c

d

e

e'(b')

d'(c')

a'

25

a

45°

m1 m

m1mLocus of M

ba

c

d

e

30°a'

b'

c'd'

e'

24. A pentagonal lamina of sides 25mm is having a side both on HP and VP. The corner opposite to the side on which it rests is 15mm above HP. Draw the top and front views of the lamina.


X YVPHP

25

ba

c

d

e'(a') d'(b')

e

c' e'(a')d'(b')

c'

ba

c

de

θ

b

a

c

d

ea'

b'c'

d'

e'

Ans: Lamina Inclination : HP = 23°

15

25. A pentagonal lamina of sides 25mm is having a side both on HP and VP. The surface of the lamina is inclined at an angle of 60° with HP. Draw the top and front views of the lamina.


X YVPHP

25

ba

c

d

e'(a') d'(b')

e

c' e'(a')

d'(b')

c'

ba

c

de

60°

b

a

c

d

ea'

b'

c'

d'

e'

26. A regular pentagonal lamina of 25mm side is resting on one of its corners on HP while the side opposite to this corner touches VP. If the lamina makes an angle of 60° with HP and 30° with VP, draw the projections of the lamina.


X YVPHP

bc

d

e'(b') d'(c')

e

a'

b

a

c

d

e

e'(b')

d'(c')

a'

25

a

60°

b

a

c d

e

a'b'

c' d'

e'

27. A pentagonal lamina having edges 25mm is placed on one of its corners on HP such that the surface makes an angle 30° with HP and perpendicular bisector of the edge passing through the corner on which the lamina rests appears to be inclined at 30° to VP. Draw the top and front views of the lamina.


X YVPHP

bc

d

e'(b') d'(c')

e

a'

b

a

c

d

e

e'(b')

d'(c')

a'

25

a

30°

mm

b

ac

de

30°a'

b'

c'd'

e'

28. A regular pentagonal lamina of 25mm side is resting on one of its sides on HP while the corner opposite to this side touches VP. If the lamina makes an angle 60° with HP and 30° with VP, draw the projections of the lamina.


X YVPHP

25

ba

c

d

e'(a') d'(b')

e

c' e'(a')

d'(b')

c'

ba

c

de

60°

b

a

c d

e

a'

b'

c'

d'

e'

29. A pentagonal lamina of the edges 25mm is resting on VP with one of its sides such that the surface makes an angle of 60° with VP. The edge on which it rests is inclined at 45° to HP. Draw its projections.


X YVPHP a(e)

a'

c

b'

c'

d'e'

a'

b'

c'

d'e'

b(d)

25

a(e)

c

b(d)

60°

45°

a'

b'

c'

d'e'

a

c

b d

e

30. A pentagonal lamina having edges 25mm is placed on one of its corners on VP such that the surface makes an angle 30° with VP and perpendicular bisector of the edge passing through the corner on which the lamina rests appears to be inclined 30° to HP. Draw the top and front views of the lamina.

X YVPHP


b(e)

a'

a

b'

c'

d'e'

a'

b'c'

d'e'

c(d)b(e)

a

c(d)

25

30°

30°

a'

b'c'

d'

e'a

b

c d

e

m'm'

31. A pentagonal lamina having edges 25mm is placed on one of its corners on VP such that the surface makes an angle 30° with VP and perpendicular bisector of the edge passing through the corner on which the lamina rests is inclined at 45° to HP. Draw the top and front views of the lamina.


X YVPHP b(e)

a'

a

b'

c'

d'e'

a'

b'c'

d'e'

c(d)b(e)

a

c(d)

25

30°

45°

m'm1'

α

Locus of Mm1'm'

a'

b'

c'

d'

e'

a

b

c d

e

32. A hexagonal lamina of 30mm sides rests on HP with one its corners touching VP and the surface inclined at 45° to it. One of its edges is inclined to HP at 30°. Draw the front and top views of the lamina in its final position.

X YVPHP


b(f)

a'

a

b'

c(e)

30

45°

c'

d'

e'f'd

b(f)a

c(e)d

a'

b' c'

d'

e'f' a'

b'

c' d'

e'

f'

e1'

ab

c

d

e

f

Locus of E

30°α

33. Draw the top and front views of a hexagonal lamina of 30mm sides having two of its edges parallel to both VP & HP and one of its edges is 10mm from each of the planes of projection. The surface of the lamina is inclined at an angle of 60° to the HP.

X YVPHP


a

b

30

c

d

e

f

f'(a')10

e'(b') d'(c') 60°f'(a')

e'(b')

d'(c')

ab

c

d

e

f

10 a

b

cd

e

f

a'

b'

c'd'

e'

f'

34. A regular hexagonal lamina of sides 30mm is lying in such a way that one of its edges touches both the reference planes. If the lamina makes 60° with HP, draw the projections of the lamina.


X YVPHP

a

b

30

c

d

e

f

f'(a') e'(b') d'(c') 60°f'(a')

e'(b')

d'(c')

ab

c

d

e

f

ab

cd

ef

a'

b'

c'd'

e'

f'

35. A regular hexagonal lamina of sides 30mm is lying in such a way that one of its sides touches both the reference planes. If the sides opposite to the side on which its rests is 45mm above HP, draw the projections of the lamina.


45

X YVPHP

a

b

30

c

d

e

f

f'(a') e'(b') d'(c') f'(a')

e'(b')

d'(c')

ab

c

d

e

f

ab

cd

ef

a'

b'

c'd'

e'

f'

36. A regular hexagonal lamina of sides 25mm is lying in such a way that one of its sides is on HP while the side opposite to the side on which it rests is on VP. If the lamina makes 60° to HP, Draw the projections of the lamina.


X YVPHP

a

b

25

c

d

e

f

f'(a') e'(b') d'(c') 60°f'(a')

e'(b')

d'(c')

ab

c

d

e

f

a

bc d

e

f

a'

b'

c' d'

e'

f'

37. A regular hexagonal lamina of side 25mm is lying in such a way that one of its corners is on HP while the corner opposite to the corner on which it rests is on VP. If the lamina makes 60° to HP, Draw the projections of the lamina.

X YVPHP


a

b

25

c

d

ef

f'(b')a' e'(c') d' 60°

a

b c

d

ef

f'(b')a'

e'(c')d'

a

b

c d e

f

a'b'

c'

d'

e'

f'

38. A hexagonal lamina of sides 30mm is resting on HP with one of its corners in VP and its surface inclined at an angle of 30° with VP. The diagonal passing through that corner which is in VP is inclined at 45° to HP. Draw the projections of the lamina.


X YVPHP b(f)

a'

a

b'

c(e)

30

30°

c'

d'

e'f'd

b(f)a

c(e)

d

a'

b' c'

d'

e'f'f'

b'

c'

e'

d'

a'

d1'

ab

cd

e

f

Locus of D

45° α

Make a note that some portion of lamina must touch XY line as lamina rests on HP

39. A hexagonal lamina of sides 30mm is resting on HP with one of its corners in VP and its surface inclined at an angle of 30° with VP. The diagonal passing through that corner which is in VP appears to be inclined at 45° to HP. Draw the projections of the lamina.


X YVPHP b(f)

a'

a

b'

c(e)

30

30°

c'

d'

e'f'd

b(f)a

c(e)

d

a'

b' c'

d'

e'f'f'

b'

c'

e'

d'

a'

ab

cd

e

f

45°

Lamina rests on HP so place a'd' on 45° with some portion of lamina (i.e., corner F) touching HP

40. A hexagonal lamina of sides 25mm rests on one of its sides on HP. The lamina makes 45° to HP and the side on which it rests makes 30° to VP. Draw its projections.


X YVPHP

a

b

25

c

d

e

f

f'(a') e'(b') d'(c') 45°f'(a')

e'(b')

d'(c')

a

b

c

d

e

f

a

bc

d

ef

a'

b'

c' d'

e'

f'30°

41. A hexagonal lamina of sides 25mm rests on one of its corners on HP. The lamina makes 45° to HP and the diagonal passing through the corner on which it rests is inclined at 30° to VP. Draw its projections.


X YVPHP

a

b

25

c

d

ef

f'(b')a' e'(c') d' 45°

a

b c

d

ef

f'(b')a'

e'(c')

d'

d

a

d1 Locus of D

b

c

e

f

30° a'b'

c'

d'

e'

f'

42. A hexagonal lamina of sides 25mm rests on one of its corners on HP. The lamina makes 45° to HP and the diagonal passing through the corner on which it rests appears to be inclined at 30° to VP. Draw its projections.


X YVPHP

a

b

25

c

d

ef

f'(b')a' e'(c') d' 45°

a

b c

d

ef

f'(b')a'

e'(c')

d'

d

a

b

c

e

f

30° a'b'

c'

d'e'

f'

43. A hexagonal lamina of sides 25mm rests on one of its sides on VP. The lamina makes 45° to VP and the side on which it rests makes 45° to HP. Draw its projections.


X YVPHP

a'

b'

25

c'

d'

e'

f'

a(f) b(e) c(d) 45°

a'

b'

c'

d'

e'

f'

a

b

c d

ef

a'

b'c'

d'

e'45°

a(f)

b(e)

c(d)

f'

44. A hexagonal lamina of sides 25mm rests on one of its sides on VP. The side opposite to the side on which it rests is 30mm in front of VP & the side on which it rests makes 45° to HP. Draw its projections. Also determine the inclination of the lamina with the reference plane.


X YVPHP

a'

b'

25

c'

d'

e'

f'

a(f) b(e) c(d)

a'

b'

c'

d'

e'

f'

a

b

c d

ef

a'

b'c'

d'

e'45°

a(f)

b(e)

c(d)

f'

30Ø

Ans: Lamina Inclination to VP = 44°

45. A hexagonal lamina of sides 25mm rests on one of its corners on HP. The corner opposite to the corner on which it rests is 35mm above HP & the diagonal passing through the corner on which it rests is inclined at 30° to VP. Draw its projections. Find the inclination of the surface with HP.


35

X YVPHP

a

b

25

c

d

ef

f'(b')a' e'(c') d' θ

a

b c

d

ef

f'(b')a'

e'(c')

d'

d

a

d1 Locus of D

b

c

e

f

30° a'b'

c'

d'

e'

f'

Ans: Lamina Inclination to HP = 45°

46. Draw the projections of a circular plate of negligible thickness of 50mm diameter resting on HP on a point A on the circumference, with its plane inclined at 45° to HP and the top view of the diameter passing through the resting point makes 60° with HP.

X YVPHP


aØ50

e'

c

45°

60°b

cd

e

fg

h

a

bc

d

e

fg

h a

b

cd

e

f

gh

h'(b') g'(c')a'

a'

b'

c'

d'e'

f'(d')

e'

h'(b')

g'(c')

a'

f'(d')

h'

g'

f'

47. A circular lamina of 50mm diameter is standing with one of its points on the rim on HP and the lamina inclined at 45° to HP. The diameter at right angles to the diameter which is passing through the point on which the lamina rests is parallel to VP. Draw its projections.


X YVPHP

aØ50

e'

c

45°

bc

d

e

fg

h

a

bc

d

e

fg

h

a b

c

de

f

g

hh'(b') g'(c')a' a' b'

c'

d'e'

f'(d')

e'

h'(b')

g'(c')

a'

f'(d')

h'

g'

f'

48. A circular lamina of 50mm diameter rests on HP such that one of its diameters is inclined at 30° to VP and 45° to HP. Draw its front and top views in this position.


X YVPHP

aØ50

e'

c

45°

bc

d

e

fg

h

a

bc

d

e

fg

h

ab

c

d

ef

g

h

h'(b') g'(c')a'

a'b'

c'

d'e'

f'(d')

e'

h'(b')

g'(c')

a'

f'(d')

h'

g'

f'

30°

Locus of E

β

49. A circular lamina inclined to VP appears in the front view as an ellipse of major axis 30mm and minor axis 15mm. The major axis is parallel to both VP and HP. One end of the minor axis is in both VP and HP. Draw the projections of the lamina and determine the inclination of the lamina with the VP.

X YVPHP


a'Ø30

b

c

de

f

g

h

b'

h' g'

d'c'

a (h) b

(g) c

(f) d

e Ø

f'

e'

aab(h)

e

c(g)

d(f)

a'

b'

h' g'

d'c'

f'

e'

a'b' h'g'

d'

c'

f'e'

15

Ans: Lamina Inclination : VP = 60°

50. A circular lamina of 30mm diameter rests on VP such that one of its diameters is inclined at 30° to VP and 45° to HP. Draw its top and front views in this position.


X YVPHP

a'Ø30

bc

d e f

gh

b'

h' g'

d'c'

a (h) b

(g) c

(f) d

ef'

e'

aab(h)

e

c(g)d(f)

a'

b'

h' g'

d'c'

f'

e' a'

b'

h'

g'

d'

c'f'

e'

30°

45° α

Locus of E

Thank You

Vtu problems projection of plane surfaces

Technology

Transcript of Vtu problems projection of plane surfaces