# VTU Problems - Projection of Solids

August 14, 2017 | Author: Yashwanth Srinivasa | Category: Polytopes, Geometric Shapes, Geometry, Mathematics

CAED...

#### Description

SOLUTIONS TO

VTU QUESTIONS

PROJECTION OF SOLIDS

PREPARED BY

PRUTHVI LOY SERRAO SUSHMITA DESAI

SELECT QUESTION

1 1 1 2 1 3 1 4 1

2 1 2 2 2 3 2 4 2

3 1 3 2 3 3 3 4 3

4 1 4 2 4 3 4 4 4

5 6 1 1 5 2 6 2 5 3 6 3 5 4 6 4 5 6

7 1 7 2 7 3 7 4 7

8 1 8 2 8 3 8 4 8

9 1 9 2 9 3 9 4 9

1 0 2 0 3 0 4 0 5 0

Problem 1 - Solution

1. A square prism 35mm sides of base and 60mm axis length rests on HP on one(p‘) ofs‘ its edges ofp the base. S ' (p‘) (o ‘) (q‘) ' Draw ther‘ projections of the prism when the(o axis is ‘) s‘ (o ‘) inclined to HP at 45° and an(q‘)edge of the base r‘ (q‘ r' inclined to VP at 30°. ) 1

1

1

60

a '

(a‘)d‘

X

(a‘) d‘

HP

35

(b‘) c‘

(o2‘ ) (b‘) c‘

p (a)

q (b)

(b )

a

o1(o2) s (d)

b ' p

d

Rests on edge – HP “Edge condition”

PROJECTION OF SOLIDS

q

o1

(b )

o1 (c )

q

p

y

c'

r

300

(o2) r (c)

o2‘

450

(o2‘ )

VP

d‘

r

s

Axis - 45 HP

a

s (o2)

(c )

d - 30 VP Base edge

PRUTHVI LOY SERRAO

Problem 2 - Solution p p 2. A square prism 35mm sides of base and 60mm axis ' ' length rests on HP on one of its corners of the base (o ‘) p‘such (o ‘)that s‘ (q‘) the r‘ two base edgess' (q‘ (q‘ s' containing the corner ) ) on which it rests make equal inclinations with HP. a a ' Draw the projections of the prism when the axis is ' r' inclined to HP at 40° and appears to be inclined to VP 60 r' d (b‘ o‘ d b' at 45°. ' ) 1

1

2

'

VP

40

0

X a'

d‘(b‘) (o2‘ )

HP

c‘

c'

q

b

q (b)

Y

c'

450

q

r

p (a)

35

o1 (o2)

r (c)

Corners (d) – HP “Corner condition”

p

(o2) a

o1

o1

r b

(c)

(c )

p s

(o2) d

Axis - 40 HP

PROJECTION OF SOLIDS

s

a

Axis - 45 VP d- apparent

PRUTHVI LOY SERRAO

Problem 3 - Solution

p

p 3. A square prism 35mm sides of base and 60mm axis ' ' length rests on HP on one of its corners of the base s' (q‘ (o ‘) p‘ such (o ‘) that s‘ (q‘) the r‘ two base edges (q‘ containing the corner s' ) ) on which it rests make equal inclinations with HP. a a ' Draw the projections of the prism when the axis is ' r' inclined to HP at 40° and inclined to VP at 30°. r' 60 1

1

d (b‘ ' )

VP

d '

o2‘

b'

400

X

Y a'

d‘ (b‘) (o2‘ )

HP

c‘ b

q (b)

p (a)

o1 (o2)

c'

c'

r (c)

β

q

p

(o2) a

q

o1

300

r

r

o1

b

(c)

(c )

p locus

s

(o2) 35

Corners (d) – HP “Corner condition”

d

Axis - 40 HP

PROJECTION OF SOLIDS

s

a

Axis TL d

Axis - 30 VP – locus method

PRUTHVI LOY SERRAO

Problem 4 - Solution

4. A square prism 35mm sides of base and 60mm axis s' length rests on HP on one(p‘) ofs‘ its edges ofp the base. ' (p‘) (o ‘) (q‘) Draw ther‘ projections of the prism when the axis is s‘ (o ‘) (o ‘) inclined to HP at 45 and to VP at (q‘)30. r‘ 1

1

1

60

X

HP

45

(o2‘ )

VP (a‘) d‘

35

q (b)

o1(o2) s (d)

(b )

a

b ' p

r (c)

d

p

q

a

o1 (c )

c' q

PROJECTION OF SOLIDS

Axis - 45 HP

300

s

(o2) (c ) d

“Edge – HP”

β

r

r

s

Y

o1

(b )

(o2)

r'

o2‘

0

(b‘) c‘

(o2‘ ) (b‘) c‘

p (a)

d‘

a '

(a‘)d‘

(q‘ )

Axis TL

locus

Axis - 30 VP – locus

PRUTHVI LOY SERRAO

Problem 5 - Solution

5. A pentagonal prism 25 mm sides of base and 60 mm p' p‘ axis length rests on HP on one of its edges of the p‘ (q‘)which (o ‘) (r‘)s‘is inclined to (q‘) t' base VP at 30. q' Draw the t‘ t‘ (o ') (o ‘) projections of the prism when the axis is inclined to (r‘)s‘ HP at 40. s' 1

1

1

60

X

(b‘)e ‘

VP HP

(r‘ )

a'

a‘ b‘

(o2‘)

e' o2'

400 a‘

(c‘)d ‘

(b‘)e (o2‘ ) (c‘)d‘ ‘ q (b)

(c)

o1 (c)

o1

(o2)

o1 (o2)

e

(d) (o2)

t a

Edge on HP

PROJECTION OF SOLIDS

s

t

p

b s

(d)

s (d) t (e)

r

300

p

a

r

q

q

r (c) p (a)

c'

b

Y

d'

Axis 40 to HP

e

Base edge 30 to VP

PRUTHVI LOY SERRAO

Problem 6 - Solution

6. A pentagonal prism 25 mm sides of base and 60 mm p‘ p' axis length rests on HP on one of its edges of the p‘ (q‘)Draw (o ‘) (r‘)s‘ t' the base. the projections (q‘) of the prism when t‘ (o ') t‘ (o ‘) axis is inclined to HP at 40 and VP at 30.(q‘ 1

1

1

)

(r‘)s‘

60

X

(b‘)e ‘

VP HP

a'

a‘ b‘

(o2‘)

s'

(r‘ ) e' o2'

400 a‘

(b‘)e (o2‘ ) (c‘)d‘ ‘ q (b)

PROJECTION OF SOLIDS

s

t s

(o2)

(d)

a

t

e

Edge on HP

0 β 30

p

o1 (d)

e

r

o1

(c)

b

(o2)

s (d) t (e)

r p

o1 (o2)

Y

q (c)

a

d' q

b

r (c) p (a)

c'

(c‘)d ‘

Axis 40 to HP

Axis TL

Axis 30 to VP

PRUTHVI LOY SERRAO

locus

Problem 7 - Solution

7. A pentagonal prism 25mm sides of base and 50mm p' (p‘)t‘ axis length rests on HP on one of its cornerst' of the (p‘)t‘ (o ‘) (q‘)s‘ that r‘ base such the two base the (o ‘) edges containing (o ’) s' corner on which it rests make (q‘)s‘ equal inclinations with (q‘ r‘ HP. Draw the projections of the prism when) the r'axis (a‘) e‘ to 50 is inclined to HP at 40 and appears e' be inclined to a' VP at 45. o’ (o ‘ ) 1

1

2

X

VP HP

Y

c‘

p

e s (d)

o1

b

r

(o2)

o1 (o2)

q r

p (c)

r (c)

45

0

q

a

t (e)

c'

c‘ b

p (a)

d'

b'

0

q (b)

25

2

(b‘)d‘

40 (a‘) e‘ (o2‘ ) (b‘)d‘

1

s

o1

(c)

t d

s

a

t

(o2) d e

Corner on HP

PROJECTION OF SOLIDS

Axis 40 to HP

Axis appears - 45 to VP PRUTHVI LOY SERRAO

Problem 8 - Solution

8. A pentagonal prism 25mm sides of base and 50mm p' axis length rests on HP on(p‘)t‘ one of its cornerst' of the (p‘)t‘ (o ‘) (q‘)s‘ that r‘ base such the two base the (o ‘) edges containing (o ’) s' corner on which it rests make (q‘)s‘ equal inclinations with (q‘ r‘ HP. Draw the projections of the prism when) the r'axis (a‘) e‘ 30.e' 50 is inclined to HP at 40  and VP at a' 1

1

1

(o2‘ )

X

(b‘)d‘

VP HP

o2’

40 (a‘) e‘ (o2‘ ) (b‘)d‘

c‘ b

s (d)

p s (c)

t d

o1

b

r

o1

(o2) e

t (e)

r

p (c)

o1 (o2)

s

a

PROJECTION OF SOLIDS

Axis 40 to HP

t

(o2) d e

Corner on HP

300

q

q

a r (c)

25

Y

c'

c‘

q (b) p (a)

d'

b'

0

Axis TL

Axis 30 to VP PRUTHVI LOY SERRAO

locus

Problem 9 - Solution p u 9. A hexagonal prism 25mmu‘(p‘) sides of base and 50mm ' (o ‘) ' (o ‘) axis length rests on HP on one of its edges. Draw the u‘(p‘) t‘(q‘) s‘(r‘) t‘(q‘) (q‘ (o ‘ to t' projections of the prism when the axis is inclined ) ) HP at 45  and appears to be inclined to VP at 40. s‘(r‘) 1

1

1

f‘(a‘)

50

(o2‘ ) e‘ (b‘)

VP (o2‘ )

X

a '

f‘(a‘)

e‘ (b‘)

b'

o2‘

d‘(c‘)

d‘(c‘)

q (b) r (c)

a (o2)

(c p )

t (e)

Edge on HP

PROJECTION OF SOLIDS

e

t

Axis 45 to HP

400

u

a

(d )

(o2) f

s

o1

(c )

s

u

r

b

r o1

(d )

f

q

Y

d'

p

q

s (d) u (f)

e' c '

b

o1 (o2)

25

s'

450

HP

p (a)

(r‘)

f'

e

Axis appears 40 to VP PRUTHVI LOY SERRAO

t

Problem 10 - Solution

u‘(p‘)

p

u 10.A hexagonal prism 25mm sides of base and 50mm ' ' ‘) u‘(p‘) (o ‘) s‘(r‘) axis t‘(q‘) length rests on HP on (oone of its edges of the (q‘ (o ‘ t' t‘(q‘) base. Draw the projections of the prism when the ) ) axis is inclined to HP at 45 and s‘(r‘) to VP a at f'30. (r‘) 1

1

1

'

f‘(a‘)

50

(o2‘ ) e‘ (b‘)

VP

b'

o2‘

s'

e'

450

X

f‘(a‘)

e‘ (b‘)(o2‘ ) d‘(c‘)

d‘(c‘)

c '

HP q (b) p (a)

b r (c)

a (o2)

o1 (o2)

25

(c )

t (e)

PROJECTION OF SOLIDS

e

o1

o1

u

a f

Edge on HP

b

r

s (d) u (f)

r

(d )

Axis 45 to HP

(o2)

s

u t

β

300

p

q (c p )

q

Y

d'

f

(d ) e

Axis TL

Axis 30 to VP PRUTHVI LOY SERRAO

s

t locus

Problem 11 - Solution

p‘

p‘ 11.A hexagonal prism 25mm sides of base and 50 mm q‘ u‘(q‘) u‘ axis length p‘ u‘(q‘) (o ‘) t‘(r‘) s‘ rests on HP on one of its corners of the ) base such that the two base(o ‘ edges containing the (o ‘) t‘(r‘) (r‘) corner on which it rests make equal inclinations with a‘ t’ (s’) a‘ s‘ f‘ HP. Draw the projections of the prism when the axis 50 b‘ of the prism is f‘(b‘) inclined to HP at 40⁰ and appears to o‘ be inclined to VP (o at‘) 45⁰. 1

1

1

2

X

e‘

c‘

400 e‘(c‘)

VP HP

2

d‘

d‘

a‘ f‘(b‘) (o2‘ )e‘(c‘) d‘

r

q q (b)

r (c)

p (a)

s (d)

(o2)

r

q

(c )

o1

(d )

s

o1

s p

b

(d p )

a

o1 (o2)

u (f)

(c )

b

t u

(o2) t (e)

Corner on HP

f

PROJECTION OF SOLIDS

(e)

u

Axis 40 to HP

t

(e)

a

y

450

f

Axis appears 45 to VP PRUTHVI LOY SERRAO

Problem 12 - Solution

p‘

p‘

12.A hexagonal prism 25mm sides of base (q‘) and 50mm u‘(q‘) u‘ p‘ axis length u‘(q‘) (o ‘) t‘(r‘) s‘ rests on HP on one of its corners of the (o ‘ ) base such that the two base edges containing (o ‘) the t‘(r‘) t’ corner on which it rests make equal inclinations with a‘ (r‘) a‘ s‘ f‘ HP. Draw the projections of the prism when the axis (s’) 50 b‘ f‘(b‘) of the prism is inclined to HP at 40 ando ‘to VP at 30. 1

1

1

2

(o2‘)

X

HP

c‘

400 e‘(c‘)

VP

e‘ d‘

d‘

a‘ f‘(b‘) (o2‘ )e‘(c‘) d‘

r

0 β 30

q q (b)

r (c)

p (a)

(c )

b

s (d)

(o2)

o1 (o2)

(c )

o1

t (e)

Corner on HP

f

PROJECTION OF SOLIDS

(e)

u

Axis 40 to HP

t

o1

(d )

s a

u (f)

p

b

(d p )

a

r

q

s

(o2)

f

t u locus

(e) Axis TL

Axis 30 to VP PRUTHVI LOY SERRAO

y

a '

Problem 13 - Solution

a '

13.A square prism 35d (b‘ mm sides of base and 60 mm axis o‘ b' d base. (o ‘ ) ) ' length is suspended freely from a corner of its (o ‘) s‘ (q‘) p‘ r‘ ' Draw the projections of the prism when the axis c' appears to be inclined to VP at 45⁰. c' 2

2

1

G p '

G

60

VP r'

X d‘(b‘) (o2‘ )

a' HP

o1 (o2)

(q‘ )

(o1‘) s' (q‘ )

b

r (c) c

o2

Y p (o1)

b (o1)

a (r )

p o2

35

Corners (d) condition

d

s

PROJECTION OF SOLIDS

c

d 45 Axis appears to VP PRUTHVI LOY SERRAO

Freely suspended

s'

450

q

q

(r ) a

(o1‘)

r'

c‘

q (b)

p (a)

p '

s

Problem 14 - Solution c' 14.A pentagonal prism 25mm sides of base and 50mm c‘ axis length is suspended freely from a corner ofd' its (b‘)d‘ (o ’) (p‘)t‘ (oDraw ‘) (q‘)s‘ the r‘ (o ‘) the prism when the base. projections of (b‘ (a‘) axis appears to be inclined to VP at 45. ) 2

1

2

e‘

50

X

r‘

G

s'

q‘

(q‘)s‘ (o1‘ )

VP HP

G

o1 '

(p‘)t‘

p'

t'

Y

(a‘) e‘ (o2‘ ) (b‘)d‘ c‘ q (b)

q

p (a)

a

b a

o1 (o2)

o2

q

c

e

(t) s

Freely suspended

PROJECTION OF SOLIDS

d (t)

(o1)

d r

Corner condition

o2

(p)

(o1)

t (e) s (d)

e

c

r

450

b

(p) r (c)

25

e'

(a‘ )

r'

s

Axis appears 45 to VP PRUTHVI LOY SERRAO

Problem 15 - Solution

a‘

a‘

f‘(b‘) f‘ 15.A hexagonal prism 25mm sides of baseb‘ and 50mm o‘ (o ‘ ) axis length is suspended freely from a corner of its u‘ t‘ e‘(c‘) e‘ (o ‘) base. Draw the projections of the c‘ prism when the (q‘) (r‘) p‘ s‘ d‘ axis appears to be inclined to VP at 45. d‘ 2

2

1

(p’)

G 50

p‘ u‘ (q‘)

G

(q’) (o1‘)

(o1‘)

X

HP

t‘

r‘

t‘(r‘)

s‘

s‘

VP a‘

f‘ (b‘)

(o2‘ )

q (b)

e‘ d‘ (c‘) c

s (d)

u (f)

b

a (s )

d o2

o1 (o2)

t (e)

e

PROJECTION OF SOLIDS

(r )

f

(t)

(r)

q

p

b p

(o1)

(s) (o1)

c

u

a (t)

o2 u

y

450

q

r (c)

p (a)

u‘

f

d e

PRUTHVI LOY SERRAO

Problem 16 - Solution

16.A square pyramid 35mm sides of base and 65mm (o ‘) ‘) o ‘ of the axis length rests on HP on (oone of its edges base which is inclined to VP at 30. Draw the projections of the pyramid when the axis is inclined a (a‘ d d ' ) ' 65to HP at 45. ' 1

1

1

(o2‘) X

VP HP

(a‘) d‘

b

a

450

(b‘ ) c‘

(o2‘ )

o2‘ Y (b‘ c' )

a

b

300 35

o1

(o2)

(o2)

d

c

c'

b'

d

o1

b

o1

c

a

c

(o2)

d

Edge on HP

Axis 45 to HP

PROJECTION OF SOLIDS

Base edge 30 to VP PRUTHVI LOY SERRAO

Problem 17 - Solution o‘ 17.A square pyramid 35mm sides o ‘ of base and 60mm o‘ axis length rests on HP on one of its corners of the a a the two base edges' containing the base such that ' corner on which it rests make equal inclinations with 60 HP. Draw the projections of the pyramid when the d (b‘ o‘ d' b' ' ) (o ‘ ) is inclined to axis of the pyramid HP at 40⁰ and VP appears to be inclined to VP at 45⁰. 400 1

1

1

2

2

X

a'

d‘(b‘) (o2‘ )

HP

c‘

c'

c'

450

b

b

o1 a

35

o1 (o2)

c a

b (o2)

(c )

(c)

o1 (o2)

d

d

a d

Corner on HP

PROJECTION OF SOLIDS

Axis 40 to HP

Axis appears 45 to VP PRUTHVI LOY SERRAO

Y

Problem 18 - Solution

o‘ o‘ o ‘ pyramid of 35 mm sides 18.A square of base and 60 mm axis length rests on HP on one of itsa corners of the a ' base such that' two base edges containing the corner 60 on which it rests make equal inclinations d'with HP. b' d (b‘ Draw the projections of the pyramid when the axis o‘ ' ) (o ‘ ) VP of the pyramid is inclined to HP at 40⁰ and to VP at 400 X 30⁰. 1

1

1

2

2

a'

d‘(b‘) (o2‘ )

HP

c‘

c'

c' b

b

300

β o1 b

a

o1 (o2)

c a

(o2)

(c )

(c)

o1

locus (o2)

35

a d

Corner on HP

d

PROJECTION OF SOLIDS

Axis 40 to HP

d

Axis TL

Axis 30 to VP PRUTHVI LOY SERRAO

Y

Problem 19 - Solution

19.A square pyramid 35 mm sides of base and 60 mm (o ‘) (o ‘) of its edges of o the ‘ axis length rests on HP on one base. Draw the projections of the pyramid when the axis is inclined to HP at 45⁰ and VP at 30⁰. 1

1

60

X

1

d‘

a '

(a‘)d‘

o2‘

(o2‘ )

VP

450

(a‘) d‘

HP

(o2‘ ) (b‘) c‘

a

b '

(b‘) c‘ b

a

b

y

c'

300

β o1

b a

35

(o2)

o1(o2) d

c

d

o1

locus (o2)

c

c d Axis TL

Edge on HP

PROJECTION OF SOLIDS

Axis 45 to HP

Axis 30 to VP PRUTHVI LOY SERRAO

Problem 20 - Solution

20.A pentagonal pyramid 25 mm sides of base and 60 o1’ mm axis length rests on HP on one of its edgeso of o1’ ‘ base which is inclined to VP at 30⁰. Draw the a is inclined projections of the pyramid when the axis ' a’ 60 to HP at 40⁰. 1

b '

(b’) e’

e’

o2‘

(o2’) X

400

VP HP

a’

(b’) e’ (o2’)

(c’) d’

b

b c a

25

(o2) (d)

d e

Edge on HP

(c’) d’

PROJECTION OF SOLIDS

e

Axis 40 to HP

y

d‘

o1 300

(c) a

o1(o2)

c'

o1

(c) b (o2) a

(d)

e

Base edge 30 to VP PRUTHVI LOY SERRAO

Problem 21 - Solution

21.A pentagonal pyramid 25 mm sides of base and 50 o’ o’ o‘ mm axis length rests on HP on one of its edges of the base. Draw the projections of the apyramid when a’ ' 50 the axis is inclined to HP at 40⁰ and VP at 30⁰. 1

1

1

b '

(b’) e’

e’

o2‘

(o2’) X

400

VP HP

a’

(b’) e’ (o2’)

(c’) d’

b

b

25

300

β (c)

c a

y

d‘

c'

(c’) d’

o1

(c) b a

o1(o2) d e

o1

(o2) (d) e

locus

(o2)

(d)

a e

Edge on HP

PROJECTION OF SOLIDS

Axis 40 to HP

Axis TL

Axis 30 to VP PRUTHVI LOY SERRAO

Problem 22 - Solution

22.A pentagonal pyramid 25 mm sides of base and 50 mm axis o ‘ on one of its corner of o ‘ length rests on HP o’ the base such that two base edges containing the corner on which it rests make equal inclinations with e' e‘ HP. Draw the (a‘) projections of the a'pyramid when the 50 axis of the pyramid is inclined to HP at 40⁰ and o’ (o ‘ ) appears to be inclined to VP at 45⁰. (b‘)d‘ d' b' 1

1

1

2

2

X

VP

HP

400 (a‘) e‘ (o2‘ ) (b‘)d‘

c‘

c'

c‘

b

450

b

a

a

25

(o2)

o1 (o2)

o1

e

e

b

(c)

c

d

d

o1 (c)

a

(o2) d e

Corner on HP

Axis 40 to HP

PROJECTION OF SOLIDS

Axis appears 45 to VP PRUTHVI LOY SERRAO

Y

Problem 23 - Solution

23.A pentagonal pyramid 25 mm sides of base and 50 o‘ ‘ o’ mm axis length rests on HP oon one of its corners of the base such that the two base edges containing the corner on (a‘) which it rests makea' equal inclinations e' e‘ 50 with HP. Draw the projections of the pyramid when (o ‘ ) o’ the axis of the pyramid is inclined to HP at 40⁰ and (b‘)d‘ d' b' VP to VP at 30⁰. 400 1

1

1

2

2

X

HP

(a‘) e‘ (o2‘ ) (b‘)d‘

c‘

c‘

β

b a c

(c)

(o2)

o1 (o2)

o1 a

d

d

o1

b (c)

e

e

Axis 40 to HP

PROJECTION OF SOLIDS

locus

(o2) d e

Corner on HP

300

b

a 25

c'

Axis TL

Axis 30 to VP PRUTHVI LOY SERRAO

Y

Problem 24 - Solution

24.A hexagonal pyramid 25mm sides of base and 50mm axis length rests on HP on one of its edges of the o‘ o ‘ the base which is inclined to VPo ‘ at 30. Draw projections of the pyramid when the axis is inclined to HP at 45. a' f' 1

1

f'(a')

50

X

VP HP

f'(a')

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

a

c

(o2‘ )

b'

e'(b') 45 ° b d'(c')

(o2‘ )

1

a

30 °

(c)

e'

o2‘

c'

d'

(c)

b

25 f

o1

(o2)

o1 (o2)

d e

Edge on HP

PROJECTION OF SOLIDS

(d)

f e

Axis 45 to HP

o1

(d) (o2)

a

e f

Base edge 30 to VP PRUTHVI LOY SERRAO

Y

Problem 25 - Solution

25.A hexagonal pyramid 25 mm sides of base and 50 o‘ ‘ o‘ mm axis olength rests on HP on one of its edges of the base. Draw the projections of the pyramid when f' 30⁰. a the axis is inclined to HP at 45⁰ and VP at 1

1

f'(a')

50

X

VP HP

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

a

c

'

(o2‘ )

b '

e'(b') 45 ° b d'(c')

(o2‘ )

f'(a')

1

a

o2‘

f

d

locus

a

PROJECTION OF SOLIDS

Axis 45 to HP

(d )

(o2)

e f

Edge on HP

o1

(c )

o1

(d)

f

e

0 β 30

(c) (o2)

o1 (o2)

Y

d'

c '

b

25

e'

e

Axis TL

Axis 30 to VP PRUTHVI LOY SERRAO

Problem 26 - Solution

26.A hexagonal pyramid 25 mm sides of base and50 O ‘ O ‘ O ‘ of mm axis length rests on HP on one of its corners the base such that the two base edges containing a‘ a‘ the corner on which it rests make equal b‘inclinations 50 ‘) with HP. Draw b‘(f the projections of f‘the pyramid when (o ‘) ‘ the axis of the pyramid is inclined to oHP at 40⁰ and c VP e‘ 400 c‘(e‘) to VP at 45⁰. appears to be inclined ‘ 1

1

1

2

X

a‘ b‘(f ‘) (o2‘) c‘(e‘)

2

d‘

d‘

d‘

450

HP f

e

f

e

o1

e a

o1 (o2) b

c

d

a

(d)

(o2)

b

c

25

Corner on HP

o1

f

(d)

a

(o2) c b

Axis 40 to HP

PROJECTION OF SOLIDS

Axis appears 45 to VP PRUTHVI LOY SERRAO

y

Problem 27 - Solution O ‘ 27.A hexagonal pyramid 25mm sides of base and 50mm O ‘ O ‘ axis length rests on HP on one of its corners of the base such thata‘ the two base edgesa‘ containing the b‘ corner on which it rests make equal inclinations with 50 b‘(f ‘) f‘ o‘ HP. Draw the projections of the pyramid when the (o ‘) axis of the pyramid is inclined to HP at 40 and VP at VP c e‘ 400 c‘(e‘) ‘ X 30. 1

1

1

2

2

a‘ b‘(f ‘) (o2‘) c‘(e‘)

d‘

d‘

d‘

HP f

f

e

e e

a

o1 (o2)

d

(d)

a

300

β

(o2)

o1

o1

f

(d) locus

b

c

(o2) b

c

25

Corner on HP

a

c b

Axis 40 to HP

PROJECTION OF SOLIDS

is Ax

Axis 30 to VP PRUTHVI LOY SERRAO

TL

y

Problem 28 - Solution

28.A square pyramid 35 mmc' sides of base and c'60 mm o‘ axis length is suspended freely from a corner of its base. Draw the projections ofd‘(b‘) the pyramid when (o ‘ the ) d (o ‘ ) at 45⁰. axis appears to be inclined to VP ' (b‘ 1

2

2

G

)

60 o1‘ 15

G

VP X a'

d‘(b‘) (o2‘ )

HP

a '

a '

o1‘

Y

c‘

b

450

b

b

a a

o1 (o2)

c

c o1

o2

a

c

o2 d

35

d

Corner condition

PROJECTION OF SOLIDS

d

o1

Axis appears 45 to VP PRUTHVI LOY SERRAO

Freely suspended

Problem 29 - Solution

d‘

d‘

29.A pentagonal pyramid 25mm sides of base and ‘ 50mmo axis length is suspended freely from a corner (e‘) c‘ c‘ (e‘) (o ‘) of its base. Draw the projections of the pyramid (o ‘) when the axis appears to beG inclined to VP at 45. 1

2

2

b‘

50

(a‘) b‘

o1 ‘

(a‘) o1 ‘

G X

12.5

VP HP

(a‘) b‘ (o2‘)(e‘) c‘

y

d‘ e

e

a

450 a

d

o1 (o2)

30

o1

d

b

Corner condition

PROJECTION OF SOLIDS

b

o2

o2 d

b c

a

e

c

c o1

Axis appears 45 to VP PRUTHVI LOY SERRAO

Freely suspended

Problem 30 - Solution

30.A hexagonal pyramid 25 d‘mm sides of based‘ and 50 o‘ mm axis length is suspended e‘(c‘)freely from e‘a corner c‘ of its base. Draw the projections of the pyramid when (o ‘ ) (o ‘) the axis appears to be inclined to VP at 45⁰. 1

2

G

a‘

o1‘

X

G

HP

(f‘)

f‘(b‘)

50

VP

2

b‘ a‘

o1‘

12.5

a‘ f‘(b‘) (o2‘ )e‘(c‘) d‘

y

450

f e c

b

c

a

b o2

d

a

f

d

o1

o1 (o2)

Corner condition

o2

e

e

b c

f

Freely suspended

PROJECTION OF SOLIDS

d

a

o1

Axis appears 45 to VP PRUTHVI LOY SERRAO

Problem 31 - Solution o‘ 31.A square pyramid 35 mm sides of base and 60 mm axis length rests on aHP on one of its slant a edges. Draw the projections ' of the pyramid when ' the axis appears to be inclined to VP at 45⁰. 1

60

d‘(b‘) (o2‘ )

b‘

o2‘

d '

VP o1‘

o1‘

X a'

d‘(b‘) (o2‘ )

HP

c‘

c'

c'

450

b

b

o1 b a

35

o1 (o2)

c c

o2

a

o1 a c

d

d

Corner condition

PROJECTION OF SOLIDS

o2 d

Slant edge

Axis appears 45 to VP PRUTHVI LOY SERRAO

Y

Problem 32 - Solution o1‘

32.A square pyramid 35mm sides of base and 60 mm a axis length rests on aHP on one of its slant edges. ' ' Draw the projections of the pyramid when the axis is inclined to VP at 45⁰. 60 d‘(b‘) (o2‘ )

b‘

o2‘

d '

VP X

a'

d‘(b‘) (o2‘ )

HP

c‘

o1‘

o1‘ Y

c'

c' b

b

β

450 o1

a

o1 (o2)

c c

o2

a

o1

b a

35

locus

o2 d

c

d

d

Corner condition

PROJECTION OF SOLIDS

Slant edge

is Ax

Axis 45 to VP PRUTHVI LOY SERRAO

TL

Problem 33 - Solution

33.A square pyramid 35 mm sides of base and 60 mm (o ‘) axis length rests o HP on one of its slant triangular faces. Draw the projections of the pyramid when the axis appears to be inclined to VP at 45⁰. 1

60

o2‘

(o2‘ ) X

VP

d‘

a '

(a‘)d‘

o1‘

(b‘)c‘ (a‘) d‘

HP

(o2‘ ) (b‘) c‘

a

o1‘

b

b

35

d

c

c'

450

a

c

o1 a

o1

o2

o1(o2)

b '

b d

o2 d c

Edge condition

PROJECTION OF SOLIDS

Slant face

Axis appears 45 to VP PRUTHVI LOY SERRAO

y

Problem 34 - Solution

34.A square pyramid 35 mm sides of base and 60 mm (o ‘) axis length rests o HP on one of its slant triangular faces. Draw the projections of the pyramid when the axis is inclined to VP at 45⁰. 1

a '

(a‘)d‘ 60 (o2‘ ) X

VP

d‘

o2‘

o1 ‘

(b‘)c‘ (a‘) d‘

HP

(o2‘ ) (b‘) c‘

a

b

b

35

d

c

c

o1 a

o1 b d

locus

o2 d

is Ax

c

Edge condition

PROJECTION OF SOLIDS

y

450

β

a

o2

o1(o2)

c'

b '

o1‘

Slant face

Axis 45 to VP PRUTHVI LOY SERRAO

TL

Problem 35 - Solution

35.A pentagonal pyramid 25mm sides of base and o ‘ 50mm axis length rests on HP on one of its slant edges. Draw the projections of the pyramid a‘ b‘ when (a‘) b‘ the axis appears to be inclined to VP at 45. 1

50

(o2‘)

o2‘

(e‘) c‘ X

VP HP

d‘ (a‘) b‘ (o2‘)(e‘) c‘

c‘

e‘

o1 ‘

o1 ‘ d‘

d‘

450 e

a

e o1

a d

o1 (o2)

30

d

o2

o1

e

a

b

b c

o2

c

d

b c

Corner condition

PROJECTION OF SOLIDS

Slant edge

Axis appears 45 to VP PRUTHVI LOY SERRAO

y

Problem 36 - Solution

36.A pentagonal pyramid 25 mm sides of base and 50 o ‘ mm axis length rests on HP on one of its slant edges. Draw the projections of the pyramid when a‘ b‘ (a‘) b‘ the axis is inclined to VP at 45⁰. 1

50

(o2‘)

o2‘

(e‘) c‘ X

VP HP

e‘

d‘ (a‘) b‘ (o2‘)(e‘) c‘

o1‘

o1 ‘ d‘

d‘

e

a

c‘

β

y

450

o1

e a o2

o1

a

e

b

b c

o2

locus

b

TL

d

d

c

c

Corner condition

PROJECTION OF SOLIDS

Slant edge

Axis 45 to VP

PRUTHVI LOY SERRAO

Ax is

d

o1 (o2)

30

Problem 37 - Solution

37.A pentagonal pyramid 25 mm sides of base and 50 o’ mm axis length rests on HP on one of its slant triangular faces. Draw the projections of the a a’ ' pyramid when the axis appears to be inclined to VP 50 at 45⁰. b (b’) e’ e’ 1

'

(o2’)

X

VP HP

a’

(b’) e’(o2’)

(c’) d’

o1’

(c’) d’

a

25

d‘

450

b c

o1 a

b

o2

o1(o2) d

o1‘ c'

b c

o2‘

o1 c

d

e

a o2

e

d

Edge condition

PROJECTION OF SOLIDS

Slant face

e

Axis appears 45 to VP PRUTHVI LOY SERRAO

y

Problem 38 - Solution o’ 38.A pentagonal pyramid 25mm sides of base and 50mm axis length rests on HP on one of its slant a a’ triangular faces. Draw the projections of the ' pyramid when the axis is inclined to VP at 45. 50 1

b '

(b’) e’ (o2’)

X

VP HP

a’

(b’) e’(o2’)

(c’) d’

a

25

o2‘ o1’

(c’) d’

o1‘

c'

d‘

y

450

β

b

b c

e’

o1

c a o1

o2

o1(o2) d

d

e

b c

e

a

d

Edge condition

PROJECTION OF SOLIDS

Slant face

locus

o2 e

Axis 45 to VP

PRUTHVI LOY SERRAO

Ax

is

TL

Problem 39 - Solution

39.A hexagonal pyramid 25 mm sides of base and 50 o‘ mm axis length rests on HP on one of its slant a‘ a‘ edges. Draw the projections when the axis appears b‘ f‘(b‘)at 45⁰. f‘ to be inclined to VP 1

50

(o2‘ ) e‘(c‘)

X

VP HP

o2‘

c‘

e‘

o1‘

d‘

o1‘ d‘

a‘ f‘(b‘) (o2‘ )e‘(c‘) d‘

y

450 c

b

c

b

o1 b

d

a

d

c

a o2

o1 (o2)

a

o1 d

f

Corner condition

e

e

PROJECTION OF SOLIDS

f

Slant edge

o2 f e

Axis appears 45 to VP PRUTHVI LOY SERRAO

Problem 40 - Solution o‘ 40.A hexagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one ofa‘ its slant a‘ edges. Draw the projections of the b‘pyramid when f‘(b‘) f‘ the axis is inclined to VP at 45⁰. 50 1

(o2‘ )

c‘

e‘(c‘) VP

o1‘

d‘

o1‘ d‘

a‘ f‘(b‘) (o2‘ )e‘(c‘) d‘

β c

b

c

d

a

o1

o2

e

b

a

o1 (o2)

f

o1

b

d

e

f

a

c

locus

o2 f

d e

Corner condition

PROJECTION OF SOLIDS

450

Slant edge

Axis 45 to VP PRUTHVI LOY SERRAO

TL

HP

e‘

Ax is

X

o2‘

y

Problem 41 - Solution

41.A hexagonal pyramid 25 mm sides of base and 50 ‘ mm axis olength rests on HP on one of its slant triangular faces. Draw the projections of the a‘ f‘ f'(a') pyramid when the axis appears to be inclined to VP at 50 45⁰. 1

e'(b')(o2‘ )

VP X HP

f'(a')

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

a

c

o1‘ c‘

b c

d

f e

o1

c

f

d

a o2

e d

Edge condition

PROJECTION OF SOLIDS

45

0

o1

o2

o1 (o2)

d‘

a b

25

e‘

o1‘

d'(c')

(o2‘ )

o2‘

b‘

Slant face

f e

Axis appears 45 to VP

PRUTHVI LOY SERRAO

Y

Problem 42 - Solution

42.A hexagonal pyramid 25mm sides of base and 50mm o ‘ rests on HP on one of its slant triangular axis length faces. Draw the projections of the pyramid when the a‘ f‘ f'(a') axis is inclined to VP at 45. 1

50

VP X HP

e'(b')(o2‘)

f'(a')

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

a

25

c

c‘

c

e

d‘

o1

f

d

PROJECTION OF SOLIDS

Y

450

o1

b c

e

a o2

d

Edge condition

β

a o2

d

f

o1‘

b

o1 (o2)

e‘

o1‘

d'(c')

(o2‘)

o2‘

b‘

Slant face

f e

Axis 45 to VP

PRUTHVI LOY SERRAO

locus

Ax

is

TL

Problem 43 - Solution

43.A cube of 40mm sides rests on HP on an edge which (a‘)b‘ a b is inclined to VP at 30. Draw the projections when ' ' (o ‘) the lateral square face containing the edge on (o ‘)which (o ‘) (d‘) (a‘) itb‘ rests makes c‘ an angle of 50 to HP. 1

1

1

(p‘) q‘

40 VP X HP

(d‘) c‘

(o2‘ ) (p‘) q‘

(o2‘ )

d (s)

a (p)

40

(s‘) r‘

o1

p '

a

s'

30

(s )

r'

d

0

y

d (s a)

(o2) (o2)

c'

q '

o2‘

500 (s‘) r‘

p

(d‘ )

c o1

o1 (r)

b (q)

c (r)

q

b

(r)

c

p

b

(o2)

q

Edge on HP

PROJECTION OF SOLIDS

Face 50 to HP

Base edge 30 to VP PRUTHVI LOY SERRAO

Problem 44 - Solution

44.A tetrahedron of 55mm sides rests on one of its b a O ‘ (a‘) b‘an edge containing that corner is corners such that ' ' O ‘ o ‘ its inclined to HP at 50 and VP at 30. Draw 55 (o ‘ ) o‘ projections. 1

1

1

2

X

V P H P

(a‘) b‘

2

500 (o2‘ )

c‘

a

c‘

c‘

β

300

a o1 o1 (o2)

55

(o2) c

(c)

o1

a

(c)

locus

(o2) b

b b

Corner on HP

PROJECTION OF

55

Slant edge 50 to Axis 30 to VP HP PRUTHVI LOY SERRAO SOLIDS

y

Problem 45 - Solution

45.A cone o of 50mm base diameter and 60mm axis ‘ length rests on HP on one of its generators. Draw its projections when thea‘ axis is inclined to VPa at 30. 1

h‘ b‘(h‘ ) c‘(g‘)(o ‘)

60

b‘

o2‘

g‘

c‘

2

d‘(f‘)

VP X

a‘ HP

b‘ (o2‘ ) c‘ (h‘) (g‘)

d‘ e‘ (f‘)

o1‘

e‘

d‘ e‘

a

f

f e

o1 (o2) b

g

h

h

e

a o2

a

o1 e

d

300 o1

g

f 50

o1‘

β

g h

f‘

b

d

c

Resting on end generator

c

PROJECTION OF SOLIDS

o2

d

b c

Axis 30 to VP PRUTHVI LOY SERRAO

locus T is x A

L

y

Problem 46 - Solution

46.A tetrahedron of sides 40mm is resting on one of its sides ono ‘HP. This side is parallel to VP and 40mm o ‘ o ‘ away from it. It is tilted about resting side such that 40 the base containing this edge is inclined at 30 to a‘ a‘ HP. Draw the projections of the solid. 1

1

X

V P

300 a‘

(o2‘ )

(o2‘)

(b‘) c‘

H P

1

o2‘ (b‘) c‘

b

c‘

b‘

b

40 o1

40

a

a

o1 (o2)

o1

(o2)

c

b (o2)

c

c

a

Edge on HP

PROJECTION OF SOLIDS

Base 30 to HP

Base edge parallel to VP* PRUTHVI LOY SERRAO

y

Problem 47 - Solution

47.A hexahedron of 30 mm sides is resting on one of its r' r' corners on HP such that one of its solid diagonals is q‘ s' perpendicular to VP.(q‘ s'Draw the projections of the ) p‘ r‘ solid.s‘ (q‘) p '

c'

30

b '

d (b‘ ' )

VP X HP

a'

d‘(b‘)

c‘ q

q (b)

r (c) p (a)

30

s (d)

Corner on HP

PROJECTION OF

p

(a )

s

a '

d

d' Y

a '

b

r

p (c‘) '

c

b

r

d

q

(a )

s

c

p

Diagonal parallel to HP Diagonal perpendicular to VP PRUTHVI LOY SERRAO SOLIDS

Problem 48 - Solution

48.A pentagonal prism of base side 25 mm and height p' t' (p‘)t‘ 50 mm is resting on HP on one of its base corners (p‘)t‘ (o ‘) (q‘)s‘ such that ther‘ top most edge is(o ‘)at a distance of (o ’)60 (q‘)s‘ mm above HP. Draw its projections, when its tops' (q‘ r‘ view of the axis is inclined at 45 to VP. ) Also, (a‘) e‘ r' 60 50 determine the inclination of the longer a' e'edge of the prism to HP which contains the resting corner. o’ (o ‘ ) 1

1

2

X

VP HP

(a‘) e‘ (o2‘ ) (b‘)d‘

Y c'

b

o1 (o2)

r

s (c)

t d

s (d)

o1

b

o1

e

t (e)

r p

(c) (o2)

450

q

q

p

a r (c)

d'

b'

c‘

q (b)

25

2

(b‘)d‘

c‘

p (a)

1

s

a

t

(o2) d e

Corner on HP

Top edge 60 mm above HP

PROJECTION OF SOLIDS

Axis appears - 45 to VP PRUTHVI LOY SERRAO

Problem 49 - Solution

c'

c'

49.A square pyramid of base sides 30mm and height 60mmo ‘ is suspended by a thread tied to one of the d‘(b‘) (o ‘ axis ) b‘ corners of its base. It is then tilted such that the d (o ‘ ) makes an angle of 45 with respect to the VP. ' G Considering the apex of the solid to be nearer to the 45 observer, draw the projections of athe solid. a 1

2

2

G

VP

'

o1‘

'

o1‘

11.25

X a'

d‘(b‘) (o2‘ )

HP

Y

c‘

b

β

b

b

450

a

a

30

o1 (o2)

c

o1

c

a

o2

d

Corner condition

PROJECTION OF SOLIDS

o2

c

d

d

Freely suspended

o1

is Ax

TL

locus

45 to VP (apex)

PRUTHVI LOY SERRAO

Problem 50 - Solution

50.A cone o of base diameter 40mm and axis length ‘ 50mm is resting on HP on a point on the o‘ o‘ circumference of its base such that its apex is 40mm a a‘ b‘ h‘ is ‘ inclined above HP and its top view of the axis at 60 to VP. Drawb‘(h‘ the(otop and front views of the solid. ‘) c‘ 50 40 ) g‘ axis when Also, determine the inclinations of the the o‘ c‘(g‘) base is nearer to the observer VP d‘(f‘) 1

1

1

2

2

f‘

X

a‘ HP

b‘ (o2‘ ) c‘ (h‘) (g‘)

d‘ e‘ (f‘)

d‘

e‘

e‘ o1

600 g h

40

a

g f

e

o1 (o2) b

d c

On HP

PROJECTION OF

h

(f) (o2)

a

(e) (d)

b c

o1

g

(f) (e)

h

(d)

(o2)

a b

c

Apex 40mm above Axis appears 60 to HP VP* PRUTHVI LOY SERRAO SOLIDS

y

Thank You