I. Burchaklar

XIV.Aylanma jismlar.

1. Slindrning yon sirtining yuzi 24π ga, hajmi esa 48π ga teng. Slindrning balandligini toping. (96–9–99)
A) 2 B) 4 C) 8 D) 3 E) 6
2. Slindrning balandligi H gat eng. Uning yon sirti yoyilganda yasovchisi diagonali bilan 60­⁰ li burchak tashkil qiladi. Slindrning hajmini toping. (98–1–52)

3. O`q kesimining yuzi 10 ga teng bo`lgan slindrning yon siritining yuzini toping. (98–5–45)
A) 10π B) 20π C) 30π D) 15π E) 12π
4. Slindrning balandligi 3 ga, o`q kesimining diagonali 5 ga teng. Asosining radiusini toping. (98–6–43)
A) 2 B) 3 C) 4 D) 5 E) 1
5. Slindr yon sirtining yoyilmasi tomoni a ga teng bo`lgan kvadratdan iborat. Slindrning hajmini toping. (98–8–52)

6. Slindrning o`q kesimi tomonlari ga teng bo`lgan kvadrat bo`lsa, uning hajmi qanchaga teng bo`ladi? (98–11–43)
A) B) 2 C) D) 4 E) 6
7. Slindrning o`q kesimi tomoni ga teng kvadratdan iborat. Uning hajmini hisoblang.
(00–10–38)
A) 27 B) 9 C) 54 D) 36 E) 18
8. Slindrning balandligi 5 ga, uning asosiga ichki chizilgan muntazam uchburchakning tomoni ga teng. Slindrning hajmini toping. (99–7–45)
A) 25π B) 35π C) 45π D) 40π E) 20π
9. Slindrning o`q kesimi diagonali 12 ga teng bo`lgan kvadratdan iborat. Uning hajmini toping. (99–8–66)

10. Slindrning yon sirti yoyilganda uning diagonali asosi tekisligi bilan 45⁰ li burchak tashkil qiladi. Slindrning yon sirti 144π² ga teng. Slindr asosining radiusini toping. (99–2–56)
A) 5 B) 4 C) 6 D) 8 E) 7
11. Slindr asosining radiusi 2 marta orttirilsa, uning hajmi necha marta ortadi? (99–1–39)
A) 4 B) 2 C) 3 D) 6 E) 5
12. Konusning yasovchisi 6 ga teng va u asos tekisligi bilan 30⁰ li burchak hosil qiladi. Konusning hajmini toping. (98–6–44)
A)9π B) π C)27π D) π E)81π
13. Konusning yasovchisi 12 ga teng va u asos tekisligi bilan 60⁰ li burchak hosil qiladi. Konus asosining radiusini toping. (98–11–90)
A) 12 B) 6 C) 3 D) 2 E) 4
14. Konus asosining radiusi 6 ga teng, yasovchi asos tekisligi bilan 30⁰ li burchak tashkil etadi. Asos markazidan yasovchisigacha bo`lgan masofani toping. (98–3–51)
A) 4 B) 3 C) 2,5 D) E)
15. Konusning yasovchisi asos tekisligi bilan 45⁰ li burchak tashkil etadi. Asosning markazidan yasovchisigacha bo`lgan masofa ga teng. Konusning balandligini toping. (98–10–98)
A) 5 B) 4 C) 7 D) 6,5 E) 6
16. Asosning radiusi R ga teng bo`lgan konusning yon sirti, asosi bilan o`q kesimi yuzalarining yig`indisiga teng. Konusning hajmini toping. (00–10–71)

17. Asos aylanasining uzunligi ga, balandligi 9 sm ga teng bo`lgan konusning hajmini toping. (96–1–52)
A) 16π B) 24 C) 16 D) 48 E) 144
18. Konus asosiga tomoni bo`lgan muntazam uchburchak ichki chizilgan. Konus yasovchisi 5 bo`lsa, uning hajmini toping. (98–5–46)
A) 8π B) 48π C) 36π D) 12π E) 4π
19. Konusning yon sirti 60π ga, to`la sirti 96π ga teng. Konusning yasovchisini toping. (98–9–55)
A) 12 B) 9 C) 8 D) 10 E) 11
20. Konusning yon sirti tekislikka yoyilganda, yoyilmaning uchidagi burchak 30⁰ ga teng bo`ladi. Konus yasovchisi asos radiusiga nisbatini toping. (00–7–52)
A) 10 B) 12 C) 11 D) 9 E) 13
21. Yasovchisi asos diametriga teng bo`lgan konusning balandligi ga teng. Konus yon sirtining yuzini toping. (99–6–22)
A) 24 B) 16π C) 12 D) E)
22. Konus o`q kesimining yuzi 8 ga, asosining radisui 2 ga teng. Konus yon sirtining yuzini hisoblang. (99–7–44)
A) 6π B) π C) π D) 5π E) 7π
23. Konusning o`q kesimi tomoni ga teng muntazam uchburchakdan iborat. Konus yon sirtining yuzini aniqlang. (00–10–46)
A) 6 B) 8 C) 12 D) 16 E) 18
24. Konusning o`q kesimi tomoni ga teng bo`lgan muntazam uchburchak bo`lsa, uning yon sirti yuzi qanchaga teng bo`ladi? (98–11–50)
A) 9 B) 18 C) 24 D) 28 E) 32
25. Konus asosining radiusi 0,5 ga teng. Konus yasovchisi bilan uning asos tekisligi orasidagi burchak qanday bo`lganda konus yon sirtining yuzi 0,5π ga teng bo`ladi? (96–3–32)
A) 30⁰ B) 60⁰ C) 45⁰ D)
E)
26. Konus asosining radiusi ga teng. Konus yasovchisi bilan uning asos tekisligi orasidagi burchak qanday bo`lganda konus yon siritining yuzi ga teng bo`ladi? (96–11–54)
A) 30⁰ B) 60⁰ C) 45⁰ D)
E)
27. Konus asosining radiusi ga teng. Konusning yasovchisi bilan uning asos tekisligi orasidagi burchak qanday bo`lganda konus yon sirtining yuzi ga teng bo`ladi? (96–12–56)
A) B) C) 45⁰
D) 30⁰ E) 60⁰
28. Kesik konus asoslarining radiuslari 1 va 5 ga teng. Agar balandligi 3 ga teng bo`lsa, uning yasovchisi qanchaga teng bo`ladi? (98–11–92)
A) 6 B) 3 C) 4 D) 5 E) 12
29. Kesik konusga shar ichki chizilgan. Konusning ustki asosining yuzi 36π ga, ostki asosiniki esa 64π ga teng. Shar siritining yuzini toping. (98–12–66)
A)172π B)100π C)144π D)156π E)192π
30. Yasovchisi 5 ga, balandligi 4 ga teng bo`lgan konus asosidan 2 ga teng masofada shu asosiga parallel tekislik bilan kesildi. Hosil bo`lgan kesimning yuzini hisoblang. (97–12–60)
A)2,25π B)3,16π C)2,64π D)1,81π E)3,26π
31. Yasovchisi 5 ga, balandligi 4 ga teng bo`lgan konus asosidan 2 ga teng masofada shu asosga parallel tekislik bilan kesildi. Hosil bo`lgan kesimning yuzini hisoblang. (97–9–58)
A)2,25π B)3,16π C)2,64π D)1,81π E)3,26π
32. Konusning balandligi 6 ga teng. Konusning asosidan 4 ga teng masofada unga parallel tekislik o`tkazilgan. Hosil bo`lgan kesim yuzining konus asosi yuziga nisbatini toping. (97–4–58)

33. Konusning o`q kesimi muntazam uchburchakdan, slindrniki esa kvadratdan iborat. Agar ularning hajmlari teng bo`lsa, to`la sirtlarining nisbati nimaga teng bo`ladi? (98–8–53)

34. Konusning o`q kesimi teng tomonli uchburchakdan, slindrniki esa kvadratdan iborat. Agar ularning to`la sirtlari tengdosh bo`lsa, hajmlarining nisbatlarini toping. (98–1–53)

35. Sirtining yuzi 16π ga teng bo`lgan sharning hajmini toping. (98–9–56)

36. Shar siritining yuzi Q bo`lsa, uning hajmi nimaga teng? (00–8–19)

37. Agar sferaning radiusi 50% orttirilsa, sfera sirtining yuzi necha foizga ko`payadi? (98–4–40)
A) 125 B) 100 C) 150 D) 75 E) 225
38. Ikkita sfera yuzlarining nisbati 2 ga teng. Bu sferalar diametrlarining nisbatini toping. (00–5–61)
A) 2 B) 4 C) 8 D) E)
39. Sharning bo`yash uchun 100 gr bo`yoq ishlatildi. Agar sharning diametric 3 marta orttirilsa, uning bo`yash uchun necha gr bo`yoq kerak bo`ladi?
(00–10–35)
A) 900 B) 300 C) 600 D) 450 E) 350
40. Sharni bo`yash uchun 50 massa birlikdagi bo`yoq ishlatildi. Agar sharning diametric 2 marta oshirilsa, uning bo`yash uchun qancha bo`yoq kerak bo`ladi? (98–11–40)
A) 100 B) 125 C) 150 D) 200 E) 250
41. Radiuslari 2; 3 va 4 ga teng bo`lgan metall sharlar eritilib, bitta shar quyiladi. Shu sharning hajmini toping. (98–7–54)
A) 144π B)396π C)99π D)116π E)132π
42. Kovak shar devorining hajmi 252π ga, devorning qalinligi 3 ga eng. Tashqi sharning radiusini toping. (00–2–43)
A) 5 B) 6 C) 4 D) 7 E) 8
43. Shardan tashqaridagi M nuqtadan uning sirtiga MN urinma o`tkazildi. M nuqtadan sharning sirtigacha bo`lgan eng qisqa masofa 6 ga, sharning markazigacha bo`lgan masofa 15 ga teng. MN ning uzunligini toping. (00–1–58)
A) 10 B) 16 C) 14 D) 12 E) 18
44. Sharning radiusi ga teng. Radiusning oxiridan u bilan 60⁰ li burchak tashkil etadigan kesuvchi tekislik o`tkazilgan. Kesimining yuzini toping.
(98–10–99)
A) 8 B) 12 C) 16 D) 14 E) 10
45. Uchburchakning tomonlari sharga urinadi. Sharning radiusi 4 ga teng. Shar markazidan uchburchak tekisligigacha masofa 3 ga teng bo`lsa, uchburchakka ichki chizilgan aylananing radiusi qanchaga teng bo`ladi? (98–11–95)
A) B) 1 C) 5 D) 3,5 E) 2
46. radiusi 13 ga teng bo`lgan shar tekislik bilan kesilgan. Agar shar markazidan kesimgacha masofa 10 ga, teng bo`lsa, kesm yuzini toping.
(98–6–46)
A) 69π B) π C) 100π D) 3 E) 9π
47. Kubning qirrasi 6 ga teng. Kubga ichki chizilgan sharning hajmini toping. (96–6–60)
A) 12π B) 36π C) 27π D) 18π E) 26π
48. To`la sirtining yuzi 72 ga teng bo`lgan kubga tashqi chizilgan sharning radiusini toping.
(96–1–53)
A) 3 B) 6 C) D) E) 4
49. Hajmi 125 bo`lgan kubga ichki chizilgan shar sirtining yuzini toping. (97–8–56)
A)125π B)25π C)24,5π D)105π E)25,5π
50. Qirrasi 12 ga teng kubga konus ichki chizilgan. Agar konusning asosi kubning pasktki asosiga ichki chizilgan bo`lsa, uchi esa yuqoridagi asosining markazida yotsa, konusning hajmini toping. (98–6–58)
A)120π B)132π C)126π D)156π E)144π
51. Ikkita qo`shni tomonlarning markazlari orasidagi masofa ga teng bo`lgan kubga tashqi chizilgan shar sirtining yuzini toping. (98–12–95)
A)28π B)36π C)48π D) E)
52. Slindr va unga tashqi chizilgan muntazam to`rtburchakli parallelepipedning balandligi 3 ga, parallelepiped asosining tomoni 4 ga teng. Slindrning hajmini toping. (97–4–59)
A)10π B)12π C)16π D)20π E)8π
53. Radiusi 5 ga teng bo`lgan sharga balandligi 8 ga teng to`rtburchakli muntazam prizma ichki chizilgan. prizmaning hajmini toping. (00–5–59)
A)136 B)144 C)169 D)172 E)184
54. Muntazam to`rtburchakli prizmaga slindr ichki chizilgan. slindr hajmining prizma hajmiga nisbatini toping. (00–1–57)

55. Muntazam to`rtburchakli prizmaga konus ichki chizilgan. konusning asosi prizmaning ostki asosida, uchi esa prizmaning ustki asosining markazida yotadi. Prizma hajmining konus hajmiga nisbatini toping. (00–7–49)

56. Uchburchakli muntazam prizmaga tashqi chizilgan slindrning yon sirti yuzining unga ichki chizilgan slindr yon sirti yuziga nisbatini toping. (98–9–54)
A) 3 B) 2 C) 1,5 D)2,5 E) 1,2
57. Muntazam tetraedrning qirrasi 1 ga teng. Shu tetraedrga tashqi chizilgan sharning radiusini toping. (99–5–50)

58. Piramidaning hajmi 25 ga, unga ichki chizilgan sharning radiusi 1,5 ga teng. Piramidaning to`la sirtini toping. (98–4–12)
A) 20 B) 15 C) 25 D) 30 E) 50
59. Piramidaning to`la sirti 60 ga, unga ichki chizilgan sharning radiusi 5 gateng. Piramidaning hajmini toping. (98–12–71)
A) 120 B) 80 C) 90 D) 100 E) 150
60. Uchburchakli muntazam piramidaga tashqi chizilgan sharning markazi uning balandligini 6 va 3 ga teng bo`lgan qismlarga ajratadi. Piramidaning hajmini toping. (00–6–51)

61. Muntazam to`rtburchakli piramida asosining tomoni 12 ga, unga ichki chizilgan sharning radiusi 3 ga teng. Piramidaning yon sirtini toping. (00–6–49)
A) 240 B) 120 C) 480 D) 360 E) 280
62. Muntazam sakkizburchakli piramidaning apofemasi 10 ga, uning asosiga ichki chizilgan doiraning yuzi 36π ga teng. Shu piramidaga ichki chizilgan sharning radiusini toping. (00–9–52)
A) 1 B) 2 C) 3 D) 4 E) 5
63. Muntazam oltiburchakli piramidaning apofemasi 5 ga, uning asosiga tashqi chiziligan doiraning yuzi 12π ga teng. Shu piramidaga ichki chizilgan sharning radisuini toping. (99–5–48)
A) 3 B) 3,2 C) 1,5 D) 2,5 E) 2,4
64. Muntazam uchburchakli piramidaga konus ichki chizilgan. Agar piramidaning yon yoqlari bilan asosi 60⁰ li burchak hosil qilib, piramidaning asosiga ichki chizilgan aylananing radiusi 16 ga teng bo`lsa, konusning yon sirtini toping.
(00–1–56)
A)524π B)512π C)536π D)514π E)518π
65. Sharga ichki chizilgan konusning asosi sharning katta doirasiga teng. Konusning o`q kesimining yuzi 9 ga teng. Sharning hajmini toping.
(00–9–7)
A) 30π B) 32π C) 42π D) 15π E) 10π
66. Sharga balandligi asosining diametriga teng bo`lgan konus ichki chizilgan. Agar konus asosing yuzi 2,4 ga teng bo`lsa, shar sirtining yuzini toping. (00–3–84)
A) 9π B) 6 C) 12,5 D) 15 E) 10π
67. Radiusi 5 ga teng bo`lgan sharga ichki chizlgan konusning balandligi 4 ga teng. Konusning hajmini toping. (99–2–55)
A) 28π B) 18π C) 24π D) 32π E) 16π
68. Balandligi 6 ga, yasovchisi 10 ga teng konusga ichki chizilgan sharning siritini toping. (99–4–48)

69. Radiusi 2 ga teng shar konusgha ichki chizilgan. Konus yasovchisi va balandligi orasidagi burchak 30⁰ ga teng. Konus yon sirtining yuzini toping.
(99–3–49)
A) 24π B) 4π C) 16π D) 18π E) 20π
70. Sharga ichki chizilgan konusning o`q kesimi teng yonli to`g`ri burchakli uchburchakdan iborat. Konusning hajmi shar hajmining qanday qismini tashkil etadi? (97–11–41)

71. Sharga konus ichki chizilgan. Konusning yasovchisi asosining diametriga teng. Shar hajmining konus hajmiga nisbatini toping.
(97–6–41)
A) 32:9 B) 8:3 C) 16:9 D) 27:4 E) 9:4
72. Radiusi 10 ga teng bo`lgan sferaga balandligi 18 ga teng bo`lgan konus ichki chizilgan. Konusning hajmini toping. (99–9–46)
A)210π B)216π C) 220π D)228π E)204π
73. Balandligi 3 ga, yasovchisi 6 ga teng bo`lgan konusga tashqi chizilgan sharning radiusini toping. (97–7–52)
A) B) 5 C) 6 D) E) 4,5
74. Sharga tashqi chizilgan kesik konusning yasovchilari o`rtalaridan o`tuvchi tekislik bilan shu kesik konus hosil qilgan kesimning yuzi 4π ga teng. Kesik konusning yasovchisini toping.
(97–9–79)
A) 2 B) 4 C) 3 D) 5 E) 6
75. Konusning balandligi 6 ga, yasovchisi 10 ga teng. Konusga ichki chizilgan sharning radiusini toping. (97–3–52)
A) 3 B) C) 4 D) E)
76. Sharga ichki chizilgan konusning asosi sharning eng katta doirasidan iborat. Sharning hajmi konusning hajmidan necha marta katta? (97–1–41)
A) 2 B) 4 C) 3 D) 1,5 E) 2,5
77. Teng tomonli slindrga radiusi 3 ga teng shar ichki chizilgan. Slindr va shar sirtlari orasida joylashgan jismning hajmini toping. (98–6–57)
A) 27π B) 24π C) 18π D) 12π E) 21
78. Yasovchisi 10 ga, asosining radiusi 6 ga teng bo`lgan konusga ichkichizilgan sharning radiusini toping. (97–10–52)
A) 3 B) 4 C) D) E)
79. Sharga ichki chizilgan konusning balandligi 3 ga, asosining radiusi ga teng. Sharning radiusini toping. (96–7–52)
A) 5 B) 6 C) D) E) 5,6
80. Sharga tashqi chizilgan kesik konusning yasovchilari o`rtalaridan o`tuvchi tekislik bilan shu kesik konus hosil qilgan kesimning yuzi 4π ga teng. Kesik konusning yasovchisini toping.
(97–12–59)
A) 2 B) 4 C) 3 D) 5 E) 6
81. Teng tomonli slindrga shar ichki chizilgan. Agar sharning hajmi ga teng bo`lsa, slindrning yon sirtini toping. (00–7–48)
A) 12π B) 13π C) 16π D) 15π E) 17π
82. O`q kesimi kavadratdan iborat slindrga ichkichizilgan sharning hajmi ga teng. Slindrning yon sirtini toping. (97–12–58)

83. Hajmi 432π bo`lgan slindrning o`q kesimi kvadratdan iborat . slindrga ichkichizilgan shar sirtining yuzini toping. (97–4–62)
A)120π B)134π C)144π D)150π E)124π
84. Katetlari 6 ba 8 ga teng bo`lgan to`g`ri burchakli uchburchakning kichik kateti atrofida aylanishidan hosil bo`lgan jismning to`la sirtini toping. (99–8–67)
A)144π B)100π C)80π D)150π E)90π
85. To`g`ri to`rtburchakni uning biror tomoni atrofida aylantirish natijasida slindr hosil qilingan. Slindr hajmini shu to`rtburchak yuzi S va asos aylanasining uzunligini C orqali ifodalang. (00–5–63)
A) B) C) SC D) 2SC E) 4SC
86. Tomonlari 2 va 4 ga teng bo`lgan to`g`ri to`rtburchak o`zining katta tomoni atrofida aylanadi. Hosil bo`lgan jismning to`la sirtini toping. (99–2–54)
A) 22π B) 23π C) 24π D) 20π E) 18π
87. Asosi a ga, asosidagi burchagi α ga teng bo`lgan teng yonli uchburchakni yon tomoni atrofida aylantirishdan hosil bo`lgan jismning hajmini toping. (00–6–50)

88. Rasmda ko`rsatilgan figurani OX o`qi atrofida aylantirishdan hosil bo`lgan jismning hajmini toping. (96–3–109)

A) 25π B) 48π C) 35π D) 45π E) 30π
89. Chizmada ko`rsatilgan figurani OX o`qi atrofida aylantirishdan hosil bo`lgan jism sirtining yuzini toping. (96–13–51)

A)120π B)135π C)130π D)132π E)133π
90. Rasmda ko`rsatilgan uchburchakning to`g`ri chiziq atrofida aylanishidan hosil bo`lgan jismning hajmini toping. (98–3–52)

A) 12π B) 24π C) 20π D) 16π E) 22π