M17. Ikki o’zgaruvchili ifodalarning qiymatini berilgan sonlar orqali toppish. Ifodaning qiymatini topish

1-masala. K nuqtadan sferagacha bo&lgan eng qisqa masofa 6 sm, eng uzoq masofa esa 16 sm. Berilgan sfera bilan chegaralangan shar katta doirasining yuzini hisoblang.
Berilgan: KA = 6 sm ; KB = 16 sm . Sdoira =?
OA = OB = R ; OK = OA + KA = R + 6 sm;
OB2 + KB2 = OK2 ; R2 + 162 = (R + 6)2 ;
R2 + 256 = R2 + 2 • R • 6 + 62 ; 256 = 12R + 36 ;
12R = 256 — 36 ; 12R = 220 ; 3R = 55 ;
55
/55y 3025n
doira = nR2 = — ) =—-—= 336-n . Javob: 5,
9
1
9
1
= 336 —n. 9
2-masala. Uchburchakli muntazam piramidaning balandligi 4 ga, asosining balandligi esa 4,5 ga teng. Piramidaning yon qirrasini toping.
Berilgan: h = OS = 4; h± = AD = 4,5 . I = AS =?
AO + OD = AD ; R + r = 4,5 ; R =
2a^3 + a^3
+ = 4,5 ;
3
6
6
3 & 6 &
3a^3
= 4,5 ; —— = 4,5 ; 6
aV3 = 9 ;
9 9^3 rr
a = — = ^ r- = — = 3V3 ;
- - - 3 ,
_ aV3 _ 3^3-^3 _3-3 _9 _
R = ~T = 3 = ~ = s = 3 ;
l = ^R2 + h2 = V32 + 42 = V9+16 = V25 = 5 . Javob: 1 = 5 .
3-masala. Kesik konusga uchburchakli muntazam kesik piramida ichki chizilgan, ya&ni piramida asoslari kesik konus asoslariga ichki chizilgan (95 - rasm). Kesik konus asoslarining radiuslari 2 sm va 5 sm, balandligi esa 4 sm ga teng. Piramidaning to&la sirtini toping.
Berilgan: AB = BC = AC = a; A1B1 = B1C1 = A1C1 = b ;
R1 = 2 sm; R2 = 5 sm; h = AH = 4 sm .
S , — 7 ^to&la ~m
3
6 6V3
-= 2 ; aV3 = 6 ; a = —= =-= 2V3 sm;
3 V3 3
1ABC
_a2V3 _(2V3 ) -V3_12V3_3j4 4 4
PABC = 3a = 3 • 2V3 = 6V3
4 bV3
2
2 ;
= 5; bV3=15;
15 15V3 r-b = — = —-— = 5V3 sm; V3 3
b2V3 (5V3) •Vä 75V3
A1B1C1 444
PAlBlcx = 3b = 3 • 5V3 sm = 15V3 sm; A1H = R2 — R1 = 5 sm — 2 sm = 3 sm;
I = Vh2 + (A1H)2 = = V16 + 9 = V25 = 5 sm;