Aylana va doira

3.6.2 Aylananing uzunligi.
1. Aylananing 6√3 ga teng bo’lgan vatari li yoyni tortib turadi. Aylananing uzunligini toping.
A) 12π B) 10π C) 13π D) 14π E) 9π
2. Aylananing 12√2 ga teng vatari li yoyni tortib turadi. Aylananing uzunligini toping.
A) 24π B) 20π C) 22π D) 26π E) 28π
3. Aylananing uzunligi 18π√2 ga teng.Aylanadagi AB vatar 900 li yoyni tortib turadi.
Vatarning uzunligini toping.
A) 8 B) 18 C) 16 D) 15 E) 8, 5
4. Teng yonli to’g’ri burchakli uchburchakning kateti uzunligi a ga teng bo’lgan aylananing diametriga teng. Gipotenuzaning uzunligini toping.
A) √π 2a B) π a C) 2a π D) 2 π a E) √a 2π
5. Aylanadan tashqaridagi nuqtadan ungacha bo’lgan eng uzun va eng qisqa masofalar mos ravishda 6 va 2 ga teng. Aylananing uzunligini toping.
A) 2π B) π C) 4π D) 3π E) 2, 5π
3.6.3 Aylananing yoyining uzunligi.
1. α markaziy burchakka mos yoy uzunligi l = Rα.Radiusi 5 ga teng bo’lgan aylana yoyining uzunligi radiusi 2 ga teng aylana uzunligiga teng bo’lsa, hosil bo’lgan markaziy burchakni toping.
A) 120 B) 150 C) 144 D) 135 E) 148
Aylananing markaziy burchagi 100 utiralgan yoy uzunligi 10 sm bo’lsa, aylananing radiusi necha sm (π = 3 deb olinsin)?
A) 5 B) 6 C) 3 D) 2 E) 8
2. Aylananing markaziy burchagi 90, utiralgan yoy uzunligi 15 sm bo’lsa, aylananing radiusi necha sm?
A) 15 π B) 18 π C) 24 π D) 30 π E) 36 π
3. Aylananing markaziy burchagi 600, utiralgan yoy uzunligi 10 sm bo’lsa, aylananing radiusi necha sm?
A) 15 π B) 18 π C) 30 π D) 36 π E) 24 π
4. Uzunligi 30π ga teng bo’lgan aylananing 600 li yoyini tortib turuvchi yoy uzunligi qancha?
A) 12π B) 6π C) 5π D) 3π E) 7π
5. Aylananing uzunligi radiusi 4 ga, markaziy burchagiga teng yoy uzunligiga teng.
Aylananing radiusini toping.
A) B) √32 C) 2 D) 1 E) 2
6. Radiusi 8 ga teng aylananing π 8 radianga teng bo’lgan yoyining uzunligini aniqlang.
A) 64 π B) π C) 2π D) 32 π E) π 2
7. Uzunligi 10π ga teng bo’lgan aylana, radiusi 20 ga teng bo’lgan yoy shakliga keltirilgan. Hosil bo’lgan yoyning markaziy burchagini
toping.
A) 900 B) 600 C) 1200 D) 750 E) 450
8. Radiusi 32 ga teng bo’lgan aylananing 16 radianga teng yoyining uzunligini aniqlang.
A) 0, 5π B) π C) 2π D) 4π E) 6π
9. Radiusi 1 ga teng aylana uchta yoyga bo’lingan. Ularga mos markaziy burchaklar 1, 2, va 3 sonlarga proportsional. Yoylardan eng
kattasining uzunligini toping.
A) π 3 B) π C) 32 π D) 23 π E) 43 π
10. Radiuslari orasidagi burchagi 360 va radiusi uzunligi 5 ga teng bo’lgan sektor yoyining uzunligini toping.
A) 2π B) π C) π 2 D) π 3 E) 1, 5π
11.Aylananing uzunligi 8π ga teng. Uzunligi uning 900 li yoyiga teng bo’lgan aylananing radiusini toping.
A) 1 B) 2 C) 1 2 D) 3 E) 3 2
12. Aylana yoyining uzunligi aylana uzunligining 40 % ga teng. Shu yoyga tiralgan markaziy burchakni toping.
A) 720 B) 1440 C) 1240 D) 1040 E) 1360
13. Radiusi 12 ga va markaziy burchagi 1050 ga teng bo’lgan doiraviy sektorning yoyi aylana shakliga keltirilgan. Shu aylananing radiusini aniqlang.
A) 3, 5 B) 3, 2 C) 4, 5 D) 4 E) 4, 2