1. Un trunchi de con circular drept are h=8 cm,R=11 cm si r=5 cm. Calculati:
Volumul,Generatoarea,Aria Laterala.
V=πh(R²+r²+Rr)/3=π×8(11²+5²+11×5)/3=π×8(121+25+55)/3= =π×8×201/3=
=π×8×67=536π cm³
R-r=11-5=6 cm
g=√(8²+6²)=√(64+36)=√100=10 cm
Al=πg(R+r)=π×10×(11+5)=160π cm²
2. Un trunchi de con circular drept are R=6 cm,g=5 cm si r=2 cm. Calculati:
Aria Laterala,Inaltimea,Volumul.
Al=πg(R+r)=π×5×(6+2)=40π cm²
R-r=6-2=4 cm
h=√(5²-4²)=√(25+16)=√9=3 cm
V=πh(R²+r²+Rr)/3=π×3(6²+2²+6×2)/3=π×3(36+4+12)/3=52π cm³
3. Un trunchi de con circular drept are h=16 cm,g=20 cm,r=8 cm. Calculati: Raza Mare,Aria Laterala,Volumul.
R-r=√(20²-16²)=√(400-256)=√144=12 cm
R=12+r=12+8=20 cm
Al=πg(R+r)=π×20×(20+8)=560π cm²
V=πh(R²+r²+Rr)/3=π×16(20²+8²+20×8)/3=π×16(400+64+160)/3= =π×16×624/3=3328π cm³
4. Un trunchi de con circular drept are h=40 cm,g=41 cm si r=6 cm. Calculati:
Raza Mare,Volumul,Aria Totala.
R-r=√(41²-40²)=√(1681-1600)=√81=9 cm
R=9+r=9+6=15 cm
At=πg(R+r)+πR²+πr²=π×41×(15+6)+15²π+6²π=861π+225π+36π=1122π cm²
V=πh(R²+r²+Rr)/3=π×40(15²+6²+15×6)/3=π×40(225+36+90)/3= =π×40×351/3=4680π cm³
5. Un trunchi de con circular drept are r=3 cm,g=√7 cm si h=√3 cm. Calculati:
Raza Mare,Aria Laterala,Volumul.
R-r=√(√7)²-(√3)²)=√(7-3)=√4=2 cm
R=2+r=2+3=5 cm
Al=πg(R+r)=π×√7×(5+3)=8√7π cm²
V=πh(R²+r²+Rr)/3=π×√3(5²+3²+5×3)/3=π×√3(25+9+15)/3= =π×√3×49/3=16,(3)√3π cm³
6. Un trunchi de con circular drept are R=12 cm,h=8 cm si g=10 cm. Calculati:
Raza Mica,Aria Laterala,Volumul.
R-r=√(10²-8²)=√(100-64)=√36=6 cm
12-r=6 r=12-6=6 cm
Al=πg(R+r)=π×10×(12+6)=180π cm²
V=πh(R²+r²+Rr)/3=π×8(12²+6²+12×6)/3=π×8(144+36+72)/3= =π×8×252/3=672π cm³
7. Un trunchi de con circular drept are aria totala egala cu
1.890πcm2,R=25 cm si r=15 cm. Calculati: Aria
Laterala,Inaltimea,Volumul.
Al=At-πR²-πr²=1890π-25²π-15²π=1890π-625π-225π=1040π cm²
Al=πg(R+r) =πg(25+15)
g=1040π/π(25+15)=26 cm
R-r=25-15=10 cm
h=√(26²-10²)=√(676-100)=√576= 24 cm
V=πh(R²+r²+Rr)/3=π×24(25²+15²+25×15)/3=π×24(625+225+375)/3=
=π×24×1225/3=9800π cm³
8. Intr-un trunchi de con circular drept avem R+r=10 cm,g=5 cm si h=3 cm. Calculati: Aria Laterala,Razele ,Volumul.
Al=πg(R+r) =π×5×10=50π cm²
R-r=√(5²-3²)=√(25-9)=√16= 4 cm
R+r=10
2R=14
R=7
r=10-7=3
V=πh(R²+r²+Rr)/3=π×3(7²+3²+7×3)/3=π×3(49+9+21)/3=
=π×79=79π cm³
9. Intr-un trunchi de con circular drept avem R+r=14 cm,g=17 cm si h=15 cm. Calculati: Aria Laterala,R-r,Volumul.
Al=πg(R+r) =π×17×14=238π cm²
R-r=√(17²-15²)=√(289-225)=√64= 8 cm
R+r=14
2R=14+8=22
R=11
r=14-11=3
V=πh(R²+r²+Rr)/3=π×15(11²+3²+11×3)/3=π×15(121+9+33)/3=
=π×5×163=815π cm³
10. Un trunchi de con circular drept are V=268πcm3,R=7 cm si r=2 cm. Calculati: Inaltimea,Generatoarea,Aria Laterala.
V=πh(R²+r²+Rr)/3=π×h(7²+2²+7×2)/3=π×h(49+4+14)/3=
=π×h×67=268π cm³
h=268π/67π=4 cm
R-r=7-2=5
g=√(4²+5²)=√(16+25)=√41 cm
Al=πg(R+r) =π×√41(7+2)=9√41π cm²
