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geometric projection sheet, Exams of Geometry

Alexandria UniversityGeometry

examination sheet for engineering

Typology: Exams

2016/2017

Uploaded on 12/13/2017

ahmed-h-bassiouni
ahmed-h-bassiouni 🇪🇬

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ﺔـﯿـﺳﺪﻨﮭﻟا ءﺎﯾﺰﯿﻔﻟاو تﺎﯿﺿﺎﯾﺮﻟا ﻢـــﺴﻗ
ﻲﺳﺪﻨﮭﻟا طﺎﻘﺳﻻا ةدﺎﻣ۲۰۱۳- ۲۰۱٤
ﺗﻟا نﯾرﻣﻊﺑارﻟا
طﺎﻘﺳﻹا :ةدﺎﻣ ﻲﺳدﻧﮭﻟا
قﻓاوﻣﻟا تﺑﺳﻟا أدﺑﺗ ﻰﺗﻟا ةرﺗﻔﻟا ﻲﻓ۲۲-۳-۲۰۱٤
ﺔﯾﻧارودﻟا حوطﺳﻟا ﻊطﺎﻘﺗ
بﺎ�ﺗﻛﻟا لﺋﺎ�ﺳﻣ لﺣ بﻟﺎطﻟا ﻰﻠﻋأ�ﻗرﺎ) م۱٦۳،۱٦٤،۱٦٦ ،۱٦۷ ،۱٦۸ ،۱٦۹ ﺔﺣﻔ�ﺻ (
)۲٤٤:ﺔﯾﻟﺎﺗﻟا لﺋﺎﺳﻣﻟا ﻰﻟا ﺔﻓﺎﺿﻹﺎﺑ (
) ﺔﻟﺄﺳﻣ۱:( ةرﻛ ﻊطﺎﻘﺗ ﻰﻧﺣﻧﻣ لﺛﻣΦ1
ﺎھزﻛرﻣM(4,5,6) ﺎھرطﻗ فﺻﻧو4cm ىرﺧأ ةرﻛ ﻊﻣ
Φ2
ﺎھزﻛرﻣN(7,5,5) ﺎھرطﻗ فﺻﻧو3cm.
) ﺔﻟﺄﺳﻣ۲ :( ﺎھزﻛرﻣ ةرﻛ موﻠﻌﻣﻟاM(4,6,4) ﺎھرطﻗ فﺻﻧو3cm ﮫﺳأر مﺋﺎﻗ ىرﺋاد طورﺧﻣو ،S(7,5,9)
ﻰﻓ ﮫﺗدﻋﺎﻗوπ1
ﺎھرطﻗ فﺻﻧ ةرﺋاد4 cm .نﯾﺣطﺳﻟا ﻊطﺎﻘﺗ ﻰﻧﺣﻧﻣ لﺛﻣ .
) ﺔﻟﺄﺳﻣ۳ :(ﻊطﺎﻘﺗ ﻰﻧﺣﻧﻣ لﺛﻣ مﺋﺎﻗ ىرﺋاد طورﺧﻣ ﮫﺳأرS(10,5,8) ﻰﻓ ﮫﺗدﻋﺎﻗوπ1
فﺻﻧ ةرﺋاد
ﺎھرطﻗR1=4cm رﺧا طورﺧﻣ ﻊﻣ ﮫﺳأر مﺋﺎﻗ ىرﺋادM(8,6,7) ﻰﻓ ﮫﺗدﻋﺎﻗوπ1
ﺎھرطﻗ فﺻﻧ ةرﺋاد
R2=5cm.
) ﺔﻟﺄﺳﻣ٤- أ :( ﻊطﺎﻘﺗ ﻰﻧﺣﻧﻣ لﺛﻣ طورﺧﻣيرﺋاد ﮫﺳأر مﺋﺎﻗS(6,6,8) ﻰﻓ ﮫﺗدﻋﺎﻗوπ1
ةرﺋاد ﺎھرطﻗ فﺻﻧR=5
cm أ ﻊﻣﺔﻧاوطﺳ ﺎھروﺣﻣ ﺔﻣﺋﺎﻗ ﺔﯾرﺋادv[9,3]يدوﻣﻋ ﻰﻠﻋπ2
فﺻﻧو ﺎھرطﻗr =3 cm
ﺎﮭﻋﺎﻔﺗراو12 cm
.
Page 1 of 2
: ﻲﺳﺪﻨﮭﻟا طﺎﻘﺳﻻا ةدﺎﻣ ﻊﻗﻮﻣ- esqat.com-eng-http://www.alex
pf2

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۲۰۱٤ﻗﺴـــﻢ اﻟﺮﯾﺎﺿﯿﺎت واﻟﻔﯿﺰﯾﺎء اﻟﮭﻨﺪﺳـﯿـﺔ-۲۰۱۳ ﻣﺎدة اﻻﺳﻘﺎط اﻟﮭﻨﺪﺳﻲ

أﺧرى ﻛرة ﻣﻊ 4cm ﻗطرھﺎ وﻧﺻف M(4,5,6) ﻣرﻛزھﺎ Φ 1 ﻛرة ﺗﻘﺎطﻊ ﻣﻧﺣﻧﻰ ﻣﺛل :(۱ ) ﻣﺳﺄﻟﺔ .3cmوﻧﺻف ﻗطرھﺎN(7,5,5)ﻣرﻛزھﺎ Φ 2

S(7,5,9)، وﻣﺧروط داﺋرى ﻗﺎﺋم رأﺳﮫ 3cm وﻧﺻف ﻗطرھﺎ M(4,6,4) اﻟﻣﻌﻠوم ﻛرة ﻣرﻛزھﺎ :(۲ ﻣﺳﺄﻟﺔ )

. ﻣﺛل ﻣﻧﺣﻧﻰ ﺗﻘﺎطﻊ اﻟﺳطﺣﯾن.4 cmداﺋرة ﻧﺻف ﻗطرھﺎπ 1 وﻗﺎﻋدﺗﮫ ﻓﻰ

ﻧﺻف داﺋرة π 1 ﻓﻰ وﻗﺎﻋدﺗﮫ S(10,5,8) رأﺳﮫ ﻗﺎﺋم داﺋرى ﻣﺧروط ﺗﻘﺎطﻊ ﻣﻧﺣﻧﻰ ﻣﺛل :(۳ ) ﻣﺳﺄﻟﺔ داﺋرة ﻧﺻف ﻗطرھﺎπ 1 وﻗﺎﻋدﺗﮫ ﻓﻰM(8,6,7)داﺋرى ﻗﺎﺋم رأﺳﮫﻣﻊ ﻣﺧروط اﺧرR 1 =4cmﻗطرھﺎ

. R 2 =5cm

R=5ﻧﺻف ﻗطرھﺎداﺋرةπ 1 وﻗﺎﻋدﺗﮫ ﻓﻰS(6,6,8)ﻗﺎﺋم رأﺳﮫداﺋريﻣﺧروط ﻣﺛل ﻣﻧﺣﻧﻰ ﺗﻘﺎطﻊ :(أ-٤ ﻣﺳﺄﻟﺔ ) r =3 cm ﻗطرھﺎ وﻧﺻفπ 2 ﻋﻠﻰ ﻋﻣوديv[9,3] داﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﺣورھﺎ ﺳطواﻧﺔﻣﻊ أ cm .12 cm وارﺗﻔﺎﻋﮭﺎ

Page 1 of 2

http://www.alex-eng-esqat.com- ﻣﻮﻗﻊ ﻣﺎدة اﻻﺳﻘﺎط اﻟﮭﻨﺪﺳﻲ :

۲۰۱٤ﻗﺴـــﻢ اﻟﺮﯾﺎﺿﯿﺎت واﻟﻔﯿﺰﯾﺎء اﻟﮭﻨﺪﺳـﯿـﺔ-۲۰۱۳ ﻣﺎدة اﻻﺳﻘﺎط اﻟﮭﻨﺪﺳﻲ R=5ﻧﺻف ﻗطرھﺎداﺋرةπ 1 وﻗﺎﻋدﺗﮫ ﻓﻰS(9,6,8)ﻗﺎﺋم رأﺳﮫداﺋريﻣﺧروط ﻣﺛل ﻣﻧﺣﻧﻰ ﺗﻘﺎطﻊ :(ب-٤ ﻣﺳﺄﻟﺔ ) وارﺗﻔﺎﻋﮭﺎr =3 cmﻗطرھﺎوﻧﺻفπ 2 ﻋﻠﻰﻋﻣوديv[9,3]داﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﺣورھﺎﺳطواﻧﺔﻣﻊ أcm 12 cm ﺳطواﻧﺔ داﺋرﯾﺔأﺳطﺢ ﻣﻊR=4 cmوﻧﺻف ﻗطرھﺎ M(7,6,6)ﻛرة ﻣرﻛزھﺎﺗﻘﺎطﻊﻧﻰﻣﺛل ﻣﻧﺣ :(٥ ﻣﺳﺄﻟﺔ ) .r =3 cmﻧﺻف ﻗطرھﺎπ 2 ﻓﻲوﻗﺎﻋدﺗﮭﺎ داﺋرة ﺗﻘﻊ v[7,5]π 2 ﻋﻠﻰﻋﻣوديﻗﺎﺋﻣﺔ ﻣﺣورھﺎ

وﻧﺻفπ 2 ﻋﻠﻰ 60 °وﯾﻣﯾلN (6,4,4)ﯾﻣر ﺑﺎﻟﻧﻘطﺔv 1 ﻲأﻓﻘاﻟﻣﻌﻠوم أﺳطواﻧﺔ داﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﺣورھﺎ :(٦ ﻣﺳﺄﻟﺔ ) وﯾﻣﯾلE(7,6,6)ﺎﻟﻧﻘطﺔﯾﻣر ﺑv 2 ﻲأﻓﻘوﻣﺗﺻل ﺑﮭﺎ أﺳطواﻧﺔ أﺧرى داﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﺣورھﺎ4cmﻗطرھﺎ ﺳطواﻧﺗﯾن.اﻷ،ﻣﺛل ﻣﻧﺣﻧﻰ ﺗﻘﺎطﻊ ﺳطﺣﻲ3cmﻗطرھﺎوﻧﺻفπ 2 ﻋﻠﻰ^ o^150 اﺳطواﻧﺔ داﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﻊR=5cm وﻧﺻف ﻗطرھﺎ N(7,7,7)ﻣﺛل ﻣﻧﺣﻧﻰ ﺗﻘﺎطﻊ ﻛرة ﻣرﻛزھﺎ :(۷ ﻣﺳﺄﻟﺔ ) .r =2cmوﻧﺻف ﻗطرھﺎ 45 °ﺑزاوﯾﺔ π 1 وﯾﻣﯾل ﻋﻠﻰA(6,7,3)ﯾﻣر ﺑﺎﻟﻧﻘطﺔﻲ ﻣﺣورھﺎ وﺟﮭ

R=4cmداﺋرة ﻧﺻف ﻗطرھﺎπ 1 وﻗﺎﻋدﺗﮫ ﻓﻰS(6,5,8)ﻣﺧروط داﺋرى ﻗﺎﺋم رأﺳﮫﻣﺛل ﻣﻧﺣﻧﻰ ﺗﻘﺎطﻊ :( ۸ ) ﻣﺳﺄﻟﺔ .10cmوارﺗﻔﺎﻋﮭﺎr =3 cmﻗطرھﺎوﻧﺻفv[4,4]رأﺳﻲداﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﺣورھﺎ ﻣﻊ أﺳطواﻧﺔ

R 1 =3 cm ﻗطرھﺎ وﻧﺻف رأﺳﻲv[9,3] اﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﺣورھﺎد أﺳطواﻧﺔ ﻣﻧﺣﻧﻰ ﺗﻘﺎطﻊ ﻣﺛل :(۹) ﻣﺳﺄﻟﺔ π 2 وﯾﻣﯾل ﻋﻠﻰE(6,4,4)ﯾﻣر ﺑﺎﻟﻧﻘطﺔﻲﻣﺣورھﺎ أﻓﻘ اﺳطواﻧﺔ داﺋرﯾﺔ ﻗﺎﺋﻣﺔ ﻣﻊ10 cm وارﺗﻔﺎﻋﮭﺎ (اﻟﺘﻘﺎﻃﻊ ﻣﻦ اﻟﺠﻬﺔ اﻻﻣﺎﻣﻴﺔ ﻓﻘﻂ اوﺟﺪ)R 2 =3cmوﻧﺻف ﻗطرھﺎ 60 ° ﺑزاوﯾﺔ

Page 2 of 2 http://www.alex-eng-esqat.com- ﻣﻮﻗﻊ ﻣﺎدة اﻻﺳﻘﺎط اﻟﮭﻨﺪﺳﻲ :