Aylanish figuralari

AB = 2AD = 2

demak, konus sirti S_k = 9π.
Bundan, = .
Javob: .


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4 – masala. Silindrning yasovchisiga tik bo‘lgan kesimning yuzi Q ga, o‘q kesimining yuzi esa S ga teng. Bu silindrning to‘la sirtini va hajmini toping.
Yechilishi:
Masala shartiga ko‘ra, S_ABCD= S, S_asos = Q
Bundan quyidagi tengliklarni yozish mumkin:
S = AB · AD = 2AO · AD,
Q = π · AO².
Bizga ma’lumki, silindr to‘la sirti
S_t.c. = S_yon +2S_asos . Yuqori dagi tengliklardan
AO= , AD = S/2 .
Bulardan,
S_t.c = 2π · AO · AD + 2π · AO² = πS + 2Q.
Ma’lumki silindr hajmi V = π · AO² · AD ekanligidan,
V = S_t.c = πS + 2Q.
Javob: V == .
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5 – masala. Konus yon sirtining yuzi asosining yuzidan ikki marta katta. Uning o‘q kesimining yuzi Q ga teng. Konusning hajmini toping.
Yechilishi:
Masala shartiga ko‘ra S_yon = 2 · S_asoc ,
S_ABC = Q. Ma’lumki S_yon = πrℓ= π · AO · AC,
S_asoc = πr² = π · AO², S_ABC = AO · OC.
formulalar yordamida hisoblanadi. Yuqo-
ridagilarni e’tiborga olsak, ℓ= 2r ya’ni
AC = 2AO, shu bilan birga
Q = AO · = AO² · .
ekanligini topish mumkin. Bundan AO =
Konus hajmi V = π · · · = .

Adabiyot:

1. Hakimov A.
2. Xolikov Q.S
3. Ungarov B.X.
4. Abjalilov S.X.
5. www.ziyonet.uz
6. www.NUR.uz