<prompt> Acha mathcalR iwe eneo linalojumuisha seti ya pointi katika ndege ya kuratibu inayotosheleza 8 - x y le 10 na 3y - x ge 15. Wakati mathcalR inazungushwa kwenye mstari ambao mlinganyo wake ni 3y - x 15, ujazo wa solid inayotokana ni frac mpinsqrt p, ambapo m, n, na p ni nambari kamili chanya, m na n ni kubwa kiasi, na p haigawanyiki kwa mraba wa mkuu wowote. Tafuta m n p.  <response>: asyukubwa280; kuagiza grafu; min halisi 2, max 12; kalamu giza upana wa mstari1; P halisi x halisi kurudi x3 5; Q halisi x halisi kurudi 10 - absx - 8; njia p 2,P2--8,P8--12,P12, q 2,Q2--12,Q 12; jozi A 8,10, B 4.5,6.5, C 9.75,8.25, FmguuA,B,C, G2F-A; jazaA--B--C--mzunguko,rgb0.9,0.9,0.9; choragraphP,min,max,giza; choragrafuQ,min,max,giza; choraArc8,7.67,A,G,CW,giza,Mshale wa Mwisho8; choraB--C--G--cycle,linetype4 4; leboy ge x3 5,max,Pmax,E,fontsize10; leboy le 10 - x-8,max,Qmax,E,fontsize10; lebomathcalR,6,Q6,NW; shoka Lebo f; f.pfontsize8; xaxis0, max, Kupef, 6, 1; yaxis0, 10, Kupef, 5, 1; asyKutokuwepo kwa usawa ni sawa na y ge x3 5, y le 10 - x - 8. Tunaweza kuziweka sawa ili kupata pointi mbili za makutano, x3 5 10 - x - 8 Mshale mrefu wa kulia x - 8 5 - x3. Hii ina maana kwamba moja ya x - 8, 8 - x 5 - x3, ambayo tunapata kwamba x,y leftfrac 92, frac 132right, kushotofrac394, frac334kulia. Eneo mathcalR ni pembetatu, kama inavyoonyeshwa hapo juu. Inapozungushwa kuhusu mstari y x35, imara inayotokana ni muungano wa koni mbili za kulia zinazoshiriki msingi na mhimili sawa.asyukubwa200; kuagiza tatu; currentprojection mtazamo0,0,10; defaultpenlinewidth0.7; kalamu gizaupana wa mstari1.3; jozi Fxy mguu 8,10, 4.5,6.5, 9.75,8.25; triple A 8,10,0, B 4.5,6.5,0, C 9.75,8.25,0, FFxy.x,Fxy.y,0, G2F-A , HF.x,F.y,absF-A,IF.x,F.y,-absF-A; theta1 halisi 1.2, theta2 -1.7,theta3 absF-A,theta4-2.2; triple JFtheta1uniA-F0,0,absF-A2-theta122.5 ,KFtheta2unitA-F 0,0,absF-A2-theta22.5 ,LFtheta3kitengoA-F0,0,absF-A2 -theta32.5 ,MFtheta4unitA-F-0,0,absF-A2-theta42.5 ; choraC--A--B--G--mzunguko, aina ya mstari4 4 giza; kuchoraA..H..G..I..A; kuchoraC--BA--G,linetype4 4; choraJ--C--K; choraL--B--M; nuktaB; nuktaC;kitoneF; leboh_1,BF2,SE,fontsize10; leboh_2,CF2,S,fontsize10; lebor,AF2,E,fontsize10; asyAcha h_1,h_2 iashiria urefu wa koni za kushoto na kulia, mtawalia kwa hivyo h_1 h_2, na uruhusu r ionyeshe radius yao ya kawaida. Kiasi cha koni kinatolewa na frac 13 Bh; kwa kuwa koni zote mbili zina msingi sawa, basi kiasi kinachohitajika ni frac 13 cdot pi r2 cdot h_1 h_2. Umbali kutoka kwa uhakika 8,10 hadi mstari x - 3y 15 0 unatolewa na leftfrac8 - 310 15sqrt1 2 -32kulia frac7sqrt10. Umbali kati ya leftfrac 92, frac 132right na leftfrac394, frac334right umetolewa na h_1 h_2 sqrtkushotofrac184 - frac394kulia2 kushotofrac264 - frac33 4kulia2 frac7sqrt104. Kwa hivyo, jibu ni frac343sqrt10pi120 frac343pi12sqrt10 Longrightarrow 343 12 10 365. 