Matematika (24.05.2025) 2-smena

45 ta savol · saqlash uchun kiring

Matematika formulalar varaqasi / Лист формул по математике

Tenglamalar / Уравнения

ax^{2}+bx+c=0; \quad x_{1:2}=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}; \quad \begin{cases}x_{1}+x_{2}=-\frac{b}{a}\\ x_{1}\cdot x_{2}=\frac{c}{a}\end{cases}

|f(x)|+|g(x)|=|f(x)+g(x)|\Rightarrow f(x)\cdot g(x)\ge0;

\frac{Ax}{ax^{2}\pm bx-c}\pm\frac{Bx}{ax^{2}\pm dx+c}=k \quad \Rightarrow \quad \frac{A}{ax-\frac{c}{x}\pm b}\pm\frac{B}{ax+\frac{c}{x}\pm d}=k;

(ax^{2}\pm bx-c)(ax^{2}\pm dx+c)=Ax^{2} \quad \Rightarrow \quad (ax-\frac{c}{x}\pm b)(ax+\frac{c}{x}\pm d)=A;

ax+\frac{c}{x}=z

o'zgaruvchi kiritib yechiladi / решается c помошью замены

(x-a)(x-b)(x-c)(x-d) = A \quad \Rightarrow \quad a+b=c+d

bo'lsa,

t=x^{2}-(a+b)x

o'zgaruvchi kiritib yechiladi / решается c помошью замены

Qisqa ko'paytirish formulalari / Формулы сокращённого умножения

a^{2}-b^{2}=(a-b)(a+b)

(a\pm b)^{2}=(a^{2}\pm2ab+b^{2})

(a\pm b)^{3}=a^{3}\pm3a^{2}b+3ab^{2}\pm b^{3}

a^{3}\pm b^{3}=(a\pm b)(a^{2}\mp ab+b^{2})

a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+...+ab^{n-2}+b^{n-1})

a^{2n}\pm b^{2n}=(a\pm b)(a^{2n-1}\mp a^{2n-2}b+...+ab^{2n-2}\mp b^{2n-1})

a^{2n+1}\pm b^{2n+1}=(a\pm b)(a^{2n}\mp a^{2n-1}b+...+ab^{2n-1}\mp b^{2n})

(a+b)^{n}=a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+...

...+\frac{n(n-1)(n-2)\cdot...\cdot(n-(k-1))}{k!}+...+nab^{n-1}+b^{n}

Arifmetik progressiya / Арифметическая прогрессия

a_{n}=a_{n-1}+d=a_{1}+(n-1)d;

a_{n}=\frac{a_{n-k}+a_{n+k}}{2} \quad (1\le k\le n-1);

S_{n}=\frac{a_{1}+a_{n}}{2}\cdot n=\frac{2a_{1}+d(n-1)}{2}\cdot n

Geometrik progressiya / Геометрическая прогрессия

b_{n}=b_{1}\cdot q^{n-1}; \quad b_{n}^{2}=b_{n-m}\cdot b_{n+m} \quad (1\le m\le n-1);

S_{n}=\frac{b_{1}(1-q^{n})}{1-q} \quad (|q|>1);

S_{n}=\frac{b_{1}}{1-q} \quad (|q|<1);

Logarifmning xossalari / Свойства логарифмов

log_{a}1=0; \quad log_{a}(x_{1}\cdot x_{2})=log_{a}|x_{1}|+log_{a}|x_{2}|;

log_{a}\frac{x_{1}}{x_{2}}=log_{a}|x_{1}|-log_{a}|x_{2}|; \quad log_{a}b=\frac{log_{c}b}{log_{c}a};

log_{a^{q}}x^{p}=\frac{p}{q}\cdot log_{a}x; \quad log_{a}b=\frac{1}{log_{b}a};

lg10^{n}=n; \quad lne^{n}=n;

Daraja va ildiz / Степень и корень

a^{n}\cdot a^{m}=a^{m+n}; \quad a^{n}:a^{m}=a^{m-n}; \quad (a^{m})^{n}=a^{m\cdot n};

(a\cdot b)^{n}=a^{n}\cdot b^{n}; \quad (\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}; \quad a^{-n}=\frac{1}{a^{n}};

(\frac{a^{n}}{b^{m}})^{-k}=(\frac{b^{m}}{a^{n}})^{k}; \quad (-a)^{2n}=a^{2n}; \quad (-a)^{2n+1}=-a^{2n+1};

\sqrt[n]{a^{k}}=a^{\frac{k}{n}}; \quad \sqrt[n]{a^{k}\cdot b^{m}}=\sqrt[n]{a^{k}}\cdot\sqrt[n]{b^{m}};

\sqrt[n]{\frac{a^{k}}{b^{m}}}=\frac{\sqrt[n]{a^{k}}}{\sqrt[n]{b^{m}}}; \quad (\sqrt[n]{a^{m}})^{k}=\sqrt[n]{a^{mk}}; \quad \sqrt[n]{a^{n+k}}=a\sqrt[n]{a^{k}};

a^{-\frac{k}{n}}=\frac{1}{\sqrt[n]{a^{k}}}; \quad \sqrt[n]{\sqrt[m]{a^{k}}}=\sqrt[nm]{a^{k}};

\sqrt[n]{a^{k}}\cdot\sqrt[m]{b^{p}}=\sqrt[nm]{a^{km}\cdot b^{pn}}; \quad \sqrt[n]{a^{n}}=|a| \quad (n=2k);

\sqrt[2n]{(a-b)^{2n}}=\begin{cases}a-b, & a\ge b\\ b-a, & b\ge a\end{cases}

Urinma va normal tenglamasi / Уравнение касательной и нормали

y=f(x_{0})+f^{\prime}(x_{0})(x-x_{0});

y=f(x_{0})-\frac{1}{f^{\prime}(x_{0})}(x-x_{0});

Hosilaga doir formulalar va xossalari / Таблица производных и свойства

(x^{a})^{\prime}=ax^{a-1}; \quad (a^{x})^{\prime}=a^{x}ln a; \quad (e^{x})^{\prime}=e^{x};

(log_{a}x)^{\prime}=\frac{1}{x ln a}; \quad (ln x)^{\prime}=\frac{1}{x}; \quad (sin x)^{\prime}=cos x;

(cos x)^{\prime}=-sin x; \quad (tg x)^{\prime}=\frac{1}{cos^{2}x}; \quad (ctg x)^{\prime}=-\frac{1}{sin^{2}x};

(u\pm v)^{\prime}=u^{\prime}\pm v^{\prime}; \quad (k\cdot u)^{\prime}=k\cdot u^{\prime};

(u\cdot v)^{\prime}=u^{\prime}\cdot v+u\cdot v^{\prime}; \quad (\frac{u}{v})^{\prime}=\frac{u^{\prime}\cdot v-u\cdot v^{\prime}}{v^{2}};

Integralga doir formulalar va xossalari / Таблица и свойства интегралов

\int x^{n}dx=\frac{x^{n+1}}{n+1}+C; \quad \int\frac{dx}{x}=ln|x|+C;

\int e^{x}dx=e^{x}+C; \quad \int a^{x}dx=\frac{a^{x}}{lna}+C;

\int sinx dx=-cosx+C; \quad \int cosx dx=sinx+C;

\int k\cdot f(x)dx=k\cdot\int f(x)dx;

\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx;

\int_{a}^{b}f(x)dx=F(b)-F(a); \quad \int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx;

\int_{a}^{b}f(x)dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}f(x)dx \quad (a\le c\le b);

O'rta arifmetik va o'rta geometrik / Среднее арифметическое и среднее геометрическое

A=\frac{a_{1}+a_{2}+...+a_{n}}{n}; \quad G=\sqrt[n]{a_{1}\cdot a_{2}\cdot...\cdot a_{n}}

Ba'zi trigonometrik formulalar / Основные формулы тригонометрии

Asosiy trigonometrik ayniyatlar / Основные тригонометрические свойства:

sin^{2}\alpha+cos^{2}\alpha=1; \quad tg\alpha=\frac{sin\alpha}{cos\alpha}; \quad ctg\alpha=\frac{cos\alpha}{sin\alpha};

tg^{2}\alpha+1=\frac{1}{cos^{2}\alpha}; \quad ctg^{2}\alpha+1=\frac{1}{sin^{2}\alpha};

cos(\alpha\pm\beta)=cos\alpha\cdot cos\beta\mp sin\alpha\cdot sin\beta;

sin(\alpha\pm\beta)=sin\alpha\cdot cos\beta\pm cos\alpha\cdot sin\beta;

tg(\alpha\pm\beta)=\frac{tg\alpha\pm tg\beta}{1\mp tg\alpha\cdot tg\beta}; \quad ctg(\alpha\pm\beta)=\frac{ctg\alpha\cdot ctg\beta\mp1}{ctg\alpha\pm ctg\beta};

sin\alpha+sin\beta=2sin\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

sin\alpha-sin\beta=2sin\frac{\alpha-\beta}{2}cos\frac{\alpha+\beta}{2};

cos\alpha+cos\beta=2cos\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

cos\alpha-cos\beta=-2sin\frac{\alpha+\beta}{2}sin\frac{\alpha-\beta}{2};

Trigonometrik funksiyaning ba'zi burchaklardagi qiymatlari / Значения тригонометрической функции под некоторыми углами

$\alpha$	0	$\frac{\pi}{6}$	$\frac{\pi}{4}$	$\frac{\pi}{3}$	$\frac{\pi}{2}$
$\sin\alpha$	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1
$\cos\alpha$	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0

To'g'ri burchakli uchburchak uchun formulalar / Формулы для прямоугольного треугольника

a^2 + b^2 = c^2;

a = c \cdot \sin\alpha

b = c \cdot \cos\alpha;

a = b \cdot \text{tg}\alpha

Ixtiyoriy uchburchak uchun formulalar / Формулы для произвольного треугольника

S = \frac{1}{2}ab\sin\gamma

S = \sqrt{p(p - a)(p - b)(p - c)}

p = \frac{1}{2}(a + b + c); \quad S = \frac{1}{2}h_c \cdot c

\frac{\sin\alpha}{a} = \frac{\sin\beta}{b} = \frac{\sin\gamma}{c}

a^2 = b^2 + c^2 - 2bc\cos\alpha

Uchburchak uchun formulalar (umumiy) / Формулы для треугольника (общие)

S=\frac{1}{2}ab sin\gamma; \quad S=\sqrt{p(p-a)(p-b)(p-c)};

p=\frac{1}{2}(a+b+c); \quad S=\frac{1}{2}h_{c}\cdot c;

\frac{a}{sin\alpha}=\frac{b}{sin\beta}=\frac{c}{sin\gamma}=2R; \quad a^{2}=b^{2}+c^{2}-2bc cos\alpha;

To'g'ri burchakli uchburchak / прямоугольный треугольник:

a^{2}+b^{2}=c^{2}; \quad a=c\cdot sin\alpha; \quad b=c\cdot cos\alpha; \quad a=b\cdot tg\alpha;

Uchburchakka ichki va tashqi chizilgan aylana radiuslarini hisoblash formulasi /
Формула вычисления радиусов окружности, вписанной внутрь и вне треугольника

r=\frac{2S}{a+b+c}; \quad R=\frac{abc}{4S};

To'rtburchakning yuzlari uchun formulalar / Формулы граней четырехугольника

Parallelogramm / параллелограмм:

S=a\cdot h_{a}; \quad S=a\cdot b\cdot sin\alpha;

Romb / ромб:

S=\frac{1}{2}\cdot d_{1}\cdot d_{2}; \quad S=a^{2}\cdot sin\alpha;

Trapetsiya / трапеция:

S=\frac{a+b}{2}\cdot h;

Aylana va doira Doiraviy sektor va segment yuzi / Круговой сектор и сегментная грань

l=2\pi R; \quad S=\pi R^{2};

S_{sektor}=\frac{\pi R^{2}}{360}\cdot\alpha; \quad S_{segment}=\frac{R^{2}}{2}(\alpha-sin\alpha);

Vektorlar / Векторы

|\vec{a}|=\sqrt{x^{2}+y^{2}+z^{2}}

vektorning uzunligi / длина вектора

\vec{a}\cdot\vec{b}=|\vec{a}|\cdot|\vec{b}|\cdot cos\varphi

skalyar ko'paytmasi / скалярное умножение

\vec{a}\cdot\vec{b}=x_{1}\cdot x_{2}+y_{1}\cdot y_{2}

vektorlarning skalyar ko'paytmasi / скалярное произведение векторов

\vec{a}\cdot\lambda=\vec{c}(x\cdot\lambda;y\cdot\lambda;z\cdot\lambda)

Stereometriya formulalari / Формулы стереометрии

Prizma / призма | Piramida / пирамида:

V=S\cdot H; \quad V=\frac{1}{3}S\cdot H;

Kesik piramida / усеченная пирамида:

V=\frac{1}{3}h(S_{1}+\sqrt{S_{1}\cdot S_{2}}+S_{2});

Silindr / цилиндр:

S_{yon}=2\pi RH; \quad V=\pi R^{2}H;

Konus / конус:

S_{yon}=\pi R l; \quad V=\frac{1}{3}\pi R^{2}H;

Kesik konus / усеченный конус:

V=\frac{1}{3}\pi h(R_{1}^{2}+R_{1}\cdot R_{2}+R_{2}^{2});

Shar / шар:

S=4\pi R^{2}; \quad V=\frac{4}{3}\pi R^{3};

Shar segmentining hajmi / объем шар сегмента:

V=\pi H^{2}(R-\frac{H}{3});

Shar segmentining sirtining yuzi / площадь поверхности шарового сегмента:

S_{sirt}=2\pi RH;

Agar

a, b

raqamlar uchun

5a + \frac{5b}{11} = 45

o'rinli bo'lsa,

2a + b

ni toping.

Agar

\begin{cases} x = 1 + 4 + 7 + \ldots + 301 \\ y = 2 + 8 + 14 + \ldots + 602 \end{cases}

bo'lsa,

\frac{y + 2022x}{x}

ni hisoblang.

A

shahardan

B

shaharga velosipedchi 4 soatda, piyoda 12 soatda yetib boradi. Agar ular qarama-qarshi yurishsa, necha soatda uchrashishadi?

3 ta ko'ylak 2 ta shimning

90\%

ini tashkil etadi. 1 ta ko'ylak 1 ta shimning necha foizini tashkil etadi?

Quyidagi ifodaning qiymati qaysi oraliqda:

\frac{1}{\sqrt{4} + \sqrt{3}} + \frac{1}{\sqrt{5} + \sqrt{4}} + \ldots + \frac{1}{\sqrt{25} + \sqrt{24}}

Hisoblang:

\frac{4}{\sqrt{13} - 3} - \frac{9}{\sqrt{13} + 2}

O'suvchi

\{b_n\}

geometrik progressiyada

b_1 + b_4 = 70

b_2 + b_3 = 60

bo'lsa,

b_5

ni toping.

\{a_n\}

arifmetik progressiyaning birinchi hadi 124, ayirmasi

-3\frac{1}{3}

bo'lsa, progressiyaning nechta hadi natural sondan iborat bo'ladi?

Hisoblang:

\frac{(2^2)^5 \cdot 5^{10} \cdot 2}{10^8} - \frac{2^3 \cdot 2^3 \cdot 5^4 \cdot 5^2}{10^6}

10.

Ifodani soddalashtiring:

\frac{a^4 - 64}{a^2 + 8} - \frac{a^6 - 512}{a^4 + 8a^2 + 64}

11.

Hisoblang:

\operatorname{tg}\left(\arcsin\left(-\frac{1}{2}\right)\right)

12.

Kasrni soddalashtiring:

\frac{\sqrt{5} - \sqrt{3}}{\sqrt{7} - \sqrt{5} - \sqrt{3} + 1} + \frac{\sqrt{3} - \sqrt{5}}{\sqrt{7} + \sqrt{5} + \sqrt{3} + 1}

13.

Quyidagi ayniyatdan

a

ning qiymatini toping:

(\sin 4x + \cos 4x)(\sin^3 4x - \cos^3 4x) = \frac{1}{4}\sin(ax) - \cos 8x

14.

|2x + 3| < 15

tengsizlikning butun yechimlari sonini toping.

15.

\frac{5x - \lg 0{,}1}{\sqrt{2} - \sqrt[3]{3}} < 0

tengsizlik

[-10; 20]

kesmada nechta butun ildizga ega?

16.

Quyidagi tenglamalar sistemasi nechta

(x; y)

ildizga ega?

\begin{cases} \log_x y + \log_y x = 2 \\ x^2 - y = 30 \end{cases}

17.

Tenglamaning haqiqiy ildizlari yig'indisini toping:

\sqrt[3]{(x - 6)^2} + \sqrt[3]{(x + 3)^2} + \sqrt[3]{(x - 6)(x + 3)} = 3

18.

Tengsizlikning butun ildizlari yig'indisini toping:

25 \cdot 2^x - 10^x + 5^x \ge 25

19.

Tenglamaning haqiqiy ildizlari sonini toping:

x(x^2 - 2x + 4) = 2x + 1

20.

y = \sqrt{3}x - 3

y = \frac{x}{\sqrt{3}} + 3

to'g'ri chiziqlarning kesishishidan hosil bo'lgan o'tkir burchakni toping.

21.

f(x) = \frac{x^2 - x}{2}

g(x) = \frac{x - x^2}{2}

funksiyalar uchun

f(1 + x) + g(1 - x) = x^3

tenglamaning haqiqiy ildizlari yig'indisini toping.

22.

y = \left|\ln x - \log_{\sin x} \cos x\right|

funksiyaning

x_0 = \frac{\pi}{4}

nuqtadagi hosilasini toping.

23.

f(x) = \frac{2}{\sqrt{2 - x^2}}

funksiyaning

(-1; 0)

nuqtadan o'tadigan boshlang'ich funksiyasini toping.

24.

Chizmadagi shtrixlangan maydonning yuzini (

cm^2

) toping. Kvadratlar tomonlari 1 cm ga teng.

25.

ABC

BDC

to'g'ri burchakli uchburchaklar berilgan.

|AC| = |CB|

\angle CDB = 30^\circ

va gipotenuzalar

E

nuqtada kesishsa,

BED

uchburchak yuzining

ABC

uchburchak yuziga nisbatini toping.

26.

Chizmada to'g'ri burchakli uchburchak berilgan (

\angle A = 90^\circ

AD = 6

DC = 4

BE = ED = 5

). Bo'yalgan soha yuzini toping.

27.

Muntazam ko'pburchakning tomoni

2\sqrt{3}

ga va ichki chizilgan aylana radiusi 3 ga teng bo'lsa, ko'pburchakning yuzini toping.

28.

Muntazam

ABC

uchburchakda

BD

kesma o'tkazilgan va

AD = 5

DC = 3

bo'lsin. Hosil bo'lgan

ABD

CBD

uchburchaklarga ichki chizilgan aylana radiuslari yig'indisini toping.

29.

To'rtta teng tomonli uchburchaklar chizmada ko'rsatilgandek ustma-ust qo'yilgan.

B

nuqta koordinatasi

(6; 2\sqrt{3})

bo'lsa,

\overrightarrow{CF}

vektorning koordinatalari ko'paytmasini toping.

30.

Tekislikda yotmaydigan

A

nuqtadan

AB

AC

og'ma va

AH = 5

perpendikulyar to'g'ri chiziqlar tushirilgan.

AB

og'ma va

AH

perpendikulyar orasidagi burchak

60^\circ

AC

og'ma va

AH

perpendikulyar orasidagi burchak

45^\circ

bo'lsa,

B

C

nuqtalar orasidagi eng qisqa masofani toping.

31.

A

— 24 ning natural bo'luvchilari to'plami,

B

— 16 ning natural bo'luvchilari to'plami,

C

— 20 ning natural bo'luvchilari to'plami bo'lsa,

n(A) + n(B) - n(C)

ning qiymatini toping (bu yerda

n(A)

—

A

to'plamning elementlari soni).

32.

30 kishilik guruhda 8 ta ayol bor. 3 kishidan iborat guruh tuzilganda, tuzilgan guruh 2 ta erkak va 1 ta ayoldan iborat bo'lish ehtimolini toping.

Topshiriqlar (33-35) va javob variantlari (A-F) ni o'zaro moslashtiring.

33-35.

Apofemasi va asos tekisligi orasidagi burchagi

60^\circ

bo'lgan muntazam to'rtburchakli piramidaga shar ichki chizilgan. Masalani yechishda

\pi = 3

deb oling.

Javob variantlari:

\frac{1}{4}

\frac{2}{3}

\frac{1}{2}

\frac{1}{6}

\frac{3}{2}

\frac{1}{3}

36.

Quyidagi tenglama berilgan:

\lg x - \lg(x - 2) = m

a) Tenglama ildizga ega bo'lmaydigan

m

ning eng katta butun qiymatini toping.

b) Tenglama ildizga ega bo'ladigan

m

ning barcha qiymatlarini yozing.

37.

Quyidagi tenglama berilgan:

\sin^4 x + \cos^4 x = a

a) Tenglama yechimga ega bo'lmaydigan

a

ning eng kichik natural qiymatini toping.

b) Tenglama yechimga ega bo'ladigan

a

ning eng katta natural qiymatida tenglamaning

\left[-\frac{\pi}{2}; \frac{\pi}{2}\right]

oraliqdagi yechimlari soni nechta?

38.

y = f(x)

funksiya uchun

f(x) + 3f\left(\frac{1}{x}\right) = 4x

tenglik o'rinli.

f(2)

ning qiymatini toping.

f(x) = 0

tenglama nechta ildizga ega?

39.

y = f(x)

funksiya va unga

(1; 2)

nuqtada o'tkazilgan

y = kx + l

urinmasi berilgan (urinma

Ox

o'qini

x = 3

da kesadi).

f'(1)

ni toping.

h(x) = (x^3 - 2x^2 + x + 3) \cdot f(x)

bo'lsa,

h'(1)

ni toping.

40.

y = \frac{x^2}{2}

y = 2

funksiyalar berilgan.

a) Funksiyalar bilan chegaralangan yopiq soha yuzini toping.

b) Funksiyalar bilan chegaralangan yopiq sohani

OY

o'qi atrofida

360^\circ

ga aylantirishdan hosil bo'lgan jism hajmini toping. Masalani yechishda

\pi = 3

deb oling.

41.

Yarim aylanada yuzi 20 ga teng bo'lgan

ABC

to'g'ri burchakli uchburchak berilgan (

\angle C = 90^\circ

\angle B = 15^\circ

C

nuqta

MN

diametrda).

AB

MN

kesmalar o'zaro parallel.

|AB|

ni toping.

O

N

nuqtalar orasidagi masofani toping.

42.

Quyidagi chizmada 3 ta kvadrat berilgan.

\alpha

burchakning kosinusini toping.

b) Kvadratlarning tomoni 6 ga teng bo'lsa, uchburchakning yuzini toping.

43.

Quyidagi chizmada

ABCDEF

muntazam oltiburchak berilgan,

G

—

AB

tomonning o'rtasi.

a) Muntazam oltiburchakda bo'yalgan maydonning bo'yalmagan maydonga nisbatini toping.

AB = 8

bo'lsa,

DGC

uchburchakning yuzini toping.

44.

Konusga eng katta hajmli silindr ichki chizilgan. Konusning yon sirti yoyilmasi yarim doiradan iborat. Konus asosining radiusi 3 ga teng.

a) Konus yasovchisi uzunligini toping.

b) Silindrning yon sirti yuzini toping.

45.

Eni 12 sm bo'lgan to'g'ri to'rtburchak shaklidagi tunuka enidan ikkita teng uzunlikdagi qismi qayrilib tarnov yasaldi.

a) Tarnovning ko'ndalang kesim yuzi to'g'ri to'rtburchak shaklida bo'lib, eng katta yuzaga ega bo'lsa, qayrilgan qismining uzunligini toping.

b) Shu tunukadan ko'ndalang kesimi yuzi eng katta yuzali trapetsiyadan iborat bo'lgan tarnov yasalsa, trapetsiyaning yuzini toping.

Savol	A	B	C	D	E	F
33. Shar diametrining piramida balandligiga nisbatini toping.
34. Sharning to'la sirtining piramida yon sirtiga nisbatini toping.
35. Shar hajmining piramida hajmiga nisbatini toping.