Projection of Planes- Engineering Graphics

VTU#1st year# Engineering Graphics#18EGDL15/25#common to all# notes- Dr. Ramesh B T

7. Problem1Anequilateraltriangularlaminaof25msidelieswithoneofits~stge§on~Psuchthatthesurfaceof
thelaminaisinclinedtoHPat600•TheedgeonwhichitrestsisinclinedtoVPat600.Drawtheprojections.
Solution
VP
X
HP
Problem2Anequilateraltriangularlamiaof25msideliesononeofitssidesonHP.Thelaminamakes450with
HPandoneofitsmediansisinclinedat400toVP.Drawitsprojections.
Solution
VP
X
HP

8. Problem3Atriangularlaminaof25msidesrestsononeofitscornersonVPsuchthatthemedianpassingthrough
thecorneronwhichitrestsisinclinedat300toHPand450toVP.Drawitsprojections.
Solution -
Problem4Atriangularplanefigureofsides25misrestingonHPwithoneofitscorners,suchthatthesurfaceof
thelaminamakesanangleof600withHP.Ifthesideoppositetothecorneronwhichthelaminarestsmakesanangle
of300withVP,drawthetopandfrontviewsinthisposition.
Solution
VP
HP
Problem5Atriangularplanelaminaofsides25misrestingonHPwithoneofitscornerstouchingit,suchthatthe
sideoppositetothecorneronwhichitrestsis15maboveHPandmakesanangleof300withVP.Drawthetopand
frontviewsinthisposition.Alsodeterminetheinclinationofthelaminatothereferenceplane.
Solution

9. Problem6A300-6()Osetsquareof60mlongestsideissokeptsuchthatthelongestsideisinHP,makinganangle
of30°withVP.Thesetsquareitselfisinclinedat45°toHP.Drawtheprojectionsofthesetsquare.
Solution
VP
HP
Problem7Anisoscelestriangularplateofnegligiblethicknesshasbase25mlongandaltitude35.Itisso
placedonHPsuchthatinthefrontviewitisseenasaneqUilateraltriangleof25msideswiththesidethatisparallel
toVPisinclinedat45°toHP.Drawitstopandfrontviews.Alsodeterminetheinclinationoftheplatewiththereference
plane.
Solution
VP
HP

10. Problem8Asquarelaminaof40msiderestsononeofitssidesonHP.Thelaminamakes30°toHPandtheside
onwhichitrestsmakes45°toVP.Drawitsprojections.
Solution
VP a'(d') (c')b' a'(d')
XHP
Y
fd
d
c
c
q
I
L
a b a
b
c
._-
a
Problem9Asquareplateof30msidesrestsonHPsuchthatoneofthediagonalsisinclinedat30DtoHPand45°
toVP.Drawitsprojections.
Solution
VP
X
HP

11. Problem10AsquarelamiaABCDof40msiderestsoncornerCsuchthatthediagonalACappearstobeat45"to
VP.ThetwosidesBCandCDcontainingthecornerCmakeequalinclinationswithHP.Thesurfaceofthelaminamakes
30°withHP.Drawitstopandfrontviews.
Solution
xVP
HP
b1cPJ
b'(d') Cl al
I
i
~.~._+-~.
d'
---,-----
I
I
<>
170
b
,0..
Problem11Thetopviewofasquarelamiaofside30misarectangleofsides30mx20mwiththelongerside
oftherectanglebeingparalleltobothHPandVP.Drawthetopandfrontviewsofthesquarelamina.Whatisthe
inclinationofthesurfaceofthelaminawithHPandVP?
Solution
VPa'(d')
XHP
d (
c
I
c
i
!,
.~-_.

12. Problem12Arectangularlaminaofsides20mx30mrestsonHPononeofitslongeredges.Thelaminaistilted
abouttheedgeonwhichitreststillitsplanesurfaceisinclinedtHPat45°.Theedgeonwhichitrestsisinclinedat300
toVP.Drawtheprojectionsofthelamina.
Solution
VP
XHP
d c d
c
0 a
C")
b
a20
b
a
b
I
r
Problem13Arectangularlaminaof35mx20mrestsonHPononeofitsshorteredges.Thelaminaisrotated
abouttheedgeonwhichitreststillitappearsasasquareinthetopview.Theedgeonwhichthelaminarestsbeing
paralleltobothHPandVP.Drawitsprojectionsandfinditsinclinations·toHPandVP.
Solution
RPP
LSV
VPs'(d' s'
X
Y
HP
I
I
d
c d
c ./
0 ~
N
S
b s b
b c
,
..~.

13. Problem14Arectangularlaminaof35mx20mrestsonHPononeofitsshorteredges.Thelaminaisrotated
abouttheedgeonwhichitreststillitappearsasasquareinthetopview.Theedgeonwhichthelaminarestsisinclined
30°toVP.DrawitsprojectionsandfinditsinclinationtoHP.
Solution
VPa'(d')
X
HP
Problem15Arectangularlaminaofsides20mx25mhasanedgeinHPandadjoiningedgeinVP,istiltedsuch
thatthefrontviewappearsasarectangleof20mx15. Theedge,whichisinVP,is30mfromtherightprofile
plane.(a)Drawthetopview,frontviewandtheleftprofileviewinthisposition.(b)Finditsinclinationswiththe
correspondingprincipalplanes.
Solution
RPP
LSV
25
15
d' c' d' c' d" e"
0 0
N N
VP a'
X
HP d(a)

14. Problem16Thefrontviewofarectangularlaminaofsides30mx20missquareof20msides.Drawthe
projectionsanddeterminetheinclinationsofthesurfaceofthelaminawithHPandVP.
Solution
X1
RPP
1
LSV
20
d' c'
d' c'
0
et)
~
VP
0
a' b'. a'
y
X
HP d(a) c(b). a b
X,
RPP
LSV

15. Problem18Arectangularplateofnegligiblethicknessofsi~e35x20mhasoneofitsshorteredgesinVPwiththat
edgeinclinedat400toHP.Drawthetopviewifitsfrontviewisasquareofside20.
Solution ~
VP
XHP
••j
'c'
D~
le'
Problem19Apentagonallaminaofedges25misrestingonHPwithoneofitssidessuchthatthesurfacemakes
anangleof600withHP.Theedgeonwhichitrestsisinclinedat450toVP.Drawitsprojections.
Solution
VP
HP

16. Problem20Apentagonallaminaofedges25misrestingonHPwithoneofitscornerssuchthattheplanesurface
makesanangleof6()0withHP.Thetwooftheedgescontainingthecorneronwhichthelamiarestsmakeequal
inclinationswithHP.Whentheedgeoppositetothiscornermakeanangleof45°withVPandnearertotheobserver,
drawthetopandfrontviewsoftheplanelaminainthisposition.
Solution
VP
HP
Problem21Apentagonallaminaofedges25misrestingonHPwithoneofitscornerssuchthattheedge
'oppositetothiscorneris20maboveHP&makesanangleof45°withVP.Drawthetopandfrontviewsoftheplane
laminainthisposition.DeterminetheinclinationofthelaminawithHP.
Solution
X
HP

17. Problem22Apentagonallaminaofsides25misrestingononeofitsedgesonHPwiththecorneroppositetothat
edgetouchingVP.ThisedgeisparalleltoVPandthecorner,whichtouchesVP,isataheightof15maboveHP.Draw
theprojectionsofthelaminaanddeterminetheinclinationsofthelaminawithHPandVPandthedistanceatwhichthe
paralleledgeliesfromVP.
Solution
c' c'
'------b'(d')------
10
d'
a'(e') b'(d')
..•....a'(e')
VP
X
1 .HP
y
1
II
I
d bMI
,- "=t
I
e
~
101
1N!
I
a
a
b
Problem23Apentagonallaminahavingedges25misplacedononeofitscornersonHPsuchthattheperpen-
dicularbisectoroftheedgepassingthroughthecorneronwhichthelaminarestsisinclinedat300toHPand450VP.
Drawthetopandfrontviewsofthelamina.
Solution
C'(d')
cy
VPa'(e')b' c'(d')a'
X
I
HP 1
e
----r------
1
1
a
\
~
b b
,
Problem24Apentagonallaminaofsides25mishavingasidebothonHPandVP.Thecorneroppositetothe
sideonwhichitrestsis15maboveHP.Drawthetopandfrontviewsofthelamina.
Solution
VPY
HP

18. c' c'
U')
b'
a'(e') c'
.•..
a'(e') VP
X Y
HP
e
b d
U')
N
C
a
a
b b
Problem25Apentagonallaminaofsides25mishavingasidebothonHPandVP.Thesurfaceofthelaminais
inclinedatanangleof600WithHP.Drawthetopandfrontviewsofthelamina.
Solution
Problem26Aregularpentagonallaminaof25msideisrestingononeofitscornersonHPwhiletheside
oppositetothiscornertouchesVP.Ifthelaminamakesanangleof600withHPand300withVP,drawtheprojections
ofthelamina.
Solution
VPY
HP

19. Problem27Apentagonallaminahavingedges25misplacedononeofitscornersonHPsuchthatthesurface
makesanangle30°withHPandperpendicularbisectoroftheedgepassingthroughthecorneronwhichthelamina
restsappearstobeinclinedat30°toVP.Drawthetopandfrontviewsofthelamina.
Solution
VPa'(e')b'
X
HP e
Problem28Aregularpentagonallaminaof25m sideisrestingononeofitssidesonHPwhilethecorner
oppositetothissidetouchesVP.Ifthelaminamakesanangleof60°withHPand30°withVP,drawtheprojectionsof
thelamina.
Solution
d'
a'(e') b'(d')c' a'(e') VP
x
HP
Y
d
b
y
e
e a
10
N
C
ide
ons

20. Problem29Apentagonallaminaofedges25misrestingonVPwithoneofitssidessuchthatthesurfacemakes
anangleof60"withVP.Theedgeonwhichitrestsisinclinedat45°toHP.Drawitsprojections.
Solution
d'
r
e'
10
N
c'
L_
a'
b'
X
I
a(e) b(d) c
VP
HP
Problem30Apentagonallaminahavingedges25misplacedononeofitscornersonVPsuchthatthesurface
makesanangle30°withVPandperpendicularbisectoroftheedgepassingthroughthecorneronwhichthelamina
restsappearstobeinclinedat30°toHP.Drawthetopandfrontviewsofthelamina.
Solution
,
e' e'
d'
,
a'
a'
C'
c'
X
b'
VP
Y
f/
e(b) d(c) a
HP

21. Problem31Apentagonallaminahavingedges25misplacedononeofitscornersonVPsuchthatthesurface
makesanangle30°withVPandperpendicularbisectoroftheedgepassingthroughthecorneronwhichthelamina
restsisinclinedat45°toHP.Drawthetopandfrontviewsofthelamina.
Solution
,
e' d'e'
~
d'
LocusofM
- -------_.._---
e'
/
I
a'
--- ------
a'
c'
X
VP
HP
Y
a e(b} d(c} a
Problem32Ahexagonallaminaof30m sidesrestsonHPwithoneofitscornerstouchingVPandsurface
inclinedat45°toit.OneofitsedgesisinclinedtoHPat30°.Drawthefrontandtopviewsofthelaminainitsfinal
position.
Solution

22. Problem33Drawthetopandfrontviewsofahexagonallaminaof30msideshavingtwoofitsedgesparallelto
~bothverticalandhorizontalplanesandoneofitsedgesis10mfromeachoftheplanesofprojection.Thesurface
ofthelaminaisinclinedatanangleof600totheHP.
Solution
b e
d
I
I
i
01
C d
C")i
c c
o
VP-
XHP
Problem34Aregularhexagonallaminaofsides30mislyinginsuchawaythatoneofItssidestouchesboththe
referenceplanes.Ifthelaminamakes600withHP,drawtheprojectionsofthelamina.
Solution
VP
HP

23. Problem35Aregularhexagonallaminaofside30mislyinginsuchawaythatoneofItssidestouchesboththe
referenceplanes.Ifthesideoppositetothesideonwhichitrestsis45maboveHP,drawtheprojectionsofthe
lamina.
Solution
81'
I
IO!.,
I
VP
YX
HP c
8
f e
Problem36Aregularhexagonallaminaofsides25mislyinginsuchawaythatoneofitssidesonHPwhilethe
sideoppositetothesideonwhichitrestsisonVP.Ifthelaminamakes600toHP,Drawtheprojectionsofthelamina.
Solution '

24. ...,.problem37Aregularhexagonallaminaofside25mislyinginsuchawaythatoneofitscornersonHPwhilethe
/'corneroppositetothecorneronwhichitrestsisonVP.Ifthelaminamakes60°toHP,Drawtheprojectionsofthe
lamina.
Solution
VP
HP
Problem38Ahexagonallaminaofsides30m isrestingonHPwithoneofitscornersinVPanditssurface
inclinedatanangleof3QOwithVP.ThediagonalpassingthroughthatcornerwhichisinVPisinclinedat45°toHP.
Drawtheprojectionsofthelamina.
Solution
VPY
HP

25. Problem39Ahexagonallaminaofsides30misrestingonHPwithoneofitscornersinVPanditssurfaceinclined
atanangleof300withVP.ThediagonalpassingthroughthatcornerwhichisinVPappearstobeinclinedat400toHP.
Drawtheprojectionsofthelamina.
Solution
c'
s'
s'
b' VP
X Y
s d s HP
Problem40Ahexagonallaminaofsides25mrestsononeofitssidesonHP.Thelaminamakes450toHPand
thesideonwhichitrestsmakes300toVP.Drawitsprojections.
Solution
b'
VP
X y
HP
f
LO
N
b
a
a
b b

26. Problem41Ahexagonallaminaofsides25mrestsononeofitscornersonHP.Thelaminamakes45°toHPand
thediagonalpassingthroughthecorneronwhichitrestsisinclinedat30°toVP.Drawitsprojections.
Solution
D
a'b'(f)
VP
X Y
HP
f
b
8
81LocusofA
Problem42Ahexagonallaminaofsides25mrestsononeofitscornersonHP.Thelaminamakes45°toHPand
thediagonalpassingthroughthecorneronwhichitrestsappearstobeinclinedat30°toVP.Drawitsprojections.
Solution
VP
Y

27. Problem43Ahexagonallaminaofsides25mrestsononeofitssidesonVP.Thelaminamakes45°toVPandthe
sideonwhichitrestsmakes45°toHP.Drawitsprojections.
Solution
Problem44Ahexagonallaminaofsides25mrestsononeofitssidesonVP.Thesideoppositetothesideon
whichitrestsis30minfrontofVP&thesideonwhichitrestsmakes45°toHP.Drawitsprojections.Alsodetermine
theinclinationofthelaminawiththereferenceplane.
Solution
e e e
f
f
d
f
a
Il)
N
a c a
b
X
VP
Y
d HP

28. Problem45Ahexagonallaminaofsides25mrestsononeofitscornersonHP.Thecorneroppositetothecorner
onwhichitrestsis35maboveHPandthediagonalpassingthroughthecorneronwhichitrestsisinclinedat30°to
VP.Drawitsprojections.FindtheinclinationofthesurfacewithHP.
Solution
•
,
a' b'(f) c'(e') VP
X Y
~
,
I HP
fl le
b
a
alLocusofA
f
25
'c
Problem46Drawtheprojectionsofacircularplateofnegligiblethicknessof50mdiameterrestingonHPona
pointAonthecircumference,withitsplaneinclinedat45°toHPandthetopviewofthediameterpassingthroughthe
restingpointmakes60°withVP.
Solution
VP s'b'(h')c'(g')
x
HP

29. Problem47Acircularlaminaof50mdiameterisstandingwithoneofitspointsontherimonHPandthelamina
inclinedat45°toHP.Thediameteratrightanglestothediameterwhichispassingthroughthepointonwhichthe
laminarestsisparalleltoVP.Drawitsprojections.
Solution
xVP a'b'(h')c'(g')d'(f)e'
HP
Problem48Acircularlaminaof50mdiameterrestsonHPsuchthatoneofitsdiametersisinclinedat300toVP
and450toHP.Drawitstopandfrontviewsinthisposition.
Solution
VP a'b'(h')c'(g')d'(f)e'
X
HP

30. Problem49AcircularlaminaiFlGlinedtotheVPappearsinthefrontviewasanellipseofmajoraxis30mandminor
axis15.ThemajoraxisisparalleltobothHPandVP.OneendoftheminoraxisisinboththeHPandVP.Drawthe
projectionsofthelaminaanddeterminetheinclinationofthelaminawiththeVP.
Solution
VP
HP
Problem50Acircularlaminaof30mdiameterrestsonVPsuchthatoneofitsdiametersisinclinedat30°to
VPand45°toHP.Drawitstopandfrontviewsinthisposition.
Solution
VP
XHP a
h(b)
g(c)
f(d)