Mach mit Mathematik PTS, Schulbuch

b) ​ __  AB​= 36,7m (36,674…); ​ __  BC​= 57,8m (57,870…); ​ __  CD​= 54,1m (54,129…); ​ __  DE​= 49,8m (49,819…); ​ __  EF​= 26,4m (26,400…); ​ __  FG​= 31,4m (31,400…); ​ __  GA​= 51,7m (51,739…); u = 308m (308,03…); A I = 6,63 a; A II = 7,38 a (7,375); A III = 6,12 a; A IV = 6,05 a (6,045); A V = 2,64 a; A VI = 16,0 a (15,96); A VII = 5,64 a (5,635); A = 50,4 a (50,405) 1009 kreuze an: B, C, und E 1010 a 1 = 7 cm 1011 a 1 = 8 cm, b 1 = 5 cm 1012 b 1 = 10,8 cm, c 1 = 12,6 cm 1013 u 1 : u 2 = 2 : 3; A 1 : A 2 = 4 : 9 1014 b 1 = 5,25m; u = 22m; u 1 = 16,5m; u : u 1 = 4 : 3 1015 s 1 = 117,5mm 1042 ZB: Der Radius r geht vom Mittelpunkt M des Kreises bis zu einem Punkt auf der Kreislinie k. Der Durchmesser d reicht von einem Punkt der Kreislinie zu einem gegenüberliegenden Punkt der Kreislinie und geht durch den Mittelpunkt des Kreises. 1043 a) u = 18,2 dm (18,221…); A = 26,4 dm 2 (26,420…) b) u = 2,83 km (2,8274…); A = 63,6 ha (63,617…) c) u = 25,8m (25,761…); A = 52,8m 2 (52,810…) 1044 a) r = 8,92 cm (8,9206…) b) r = 1,59 cm (1,5915…) c) r = 56,4 cm (56,418…) 1045 a) A = 14,6 cm 2 (14,630…); b = 5,63 cm (5,6269…); u = 16,0 cm (16,026…) b) A = 77,6 cm 2 (77,564…); b = 23,2 cm (23,153…); u = 36,6 cm (36,553…) 1046 l 2 = 104mm (104,37…); l 1 + l 2 + l 3 = 20 cm (19,937…) 1047 a) A = 177m 2 (176,71…) b) A = 170m 2 (169,64…) c) u = 47,1m (47,123…) 1048 a) A = A 1 + A 2 = 90 a + 44,2 a = 134 a (134,17…) b) A = 2 · A 1 + 2 · A 2 = 14,4 a + 15,3 a = 29,7a (29,668…) c) l = 2 · l 1 + 2 · l 2 = 240m + 254m = 494m (494,46…) 1098 ordne so zu: 1D, 2E, 3B, 4A, 5C 1099 a) O = 15m 2 (15,04) b) O = 3,58m 2 1100 a) O = 403 cm 2 (403,44); 436 cm 2 Karton (435,71…) b) O = 73,5 dm 2 ; 79,4 dm 2 Karton (79,38) c) O = 20,3 dm 2 (20,3136); 21,9 dm 2 Karton (21,938…) 1101 a) V = 53,8m 3 (53,76); d = 6,75m (6,7475…) b) V = 51m 3 (51,03); d = 6,72m (6,7216…) 1102 h = 12 cm (12,044) 1103 a) a = 7,37 cm (7,3680…) b) a = 3,42 cm (3,4199…) c) a = 9,28 cm (9,2831…) 1104 a) a = 18 cm; O = 19,4 dm 2 (19,44) b) a = 4,3 cm (4,2998…); O = 111 cm 2 (110,93…) c) a = 12 cm; O = 864 cm 2 1126 kreuze an: A 1127 a) V = 6,24 dm 3  b) G = 2,1 dm 2 1128 V = 0,49m 3 (0,4875) 1129 a) c = 13 cm; O = 15,6 dm 2 ; V = 1,5 dm 3 b) c = 100 cm; O = 480 dm 2 ; V = 432 dm 3 1130 a) V = 877 cm 3 (876,85…); m = 2,37 kg (2,3674…) b) V = 344 cm 3 (343,72…); m = 0,93 kg (0,92805…) 1131 a) G = 2,60 dm 2 (2,5980…) b) V = 3,12 dm 3 (3,1176…) c) O = 12,4 dm 2 (12,396…); 14,9 dm 2 Material (14,875…) 1143 a) V = 4 849m 3 (4 849,0…) b) V = 10 299m 3 (10 228,6…) 1144 a) V = 1,01 fm (1,0102…) b) V = 0,119 fm (0,11908…) 1145 h 1 = 17,7 cm (17,683…); h 2 = 7,36 cm (7,3606…) 1146 M = 432 cm 2 (431,96…) 844 a) γ = 63°, α ’ = 138°, β ’ = 105°, γ ’ = 117° b) α = 58°, α ‘ = 122°, β ’ = 122°, γ ‘ = 116° 877 a) u = 17,8 cm; A = 18,9 cm 2 b) u = 14,8 cm; A = 13,4 dm 2 (13,44) 878 a) u = 19,2m; A = 23,0m 2 (23,04) b) u = 14 dm; A = 12,3 dm 2 (12,25) 879 a) a = 48,6m (48,625) b) a = 36,4m (36,417…) 880 a) a = 5,9m b) a = 4,77m (4,7749…) c) a = 3,48m (3,4785…) 881 a) A = A 1 + A 2 = 27m · 17m + 32m · 65m = 459m 2 + 2 080m 2 = 2 539m 2 ; A = 25,4 a (25,39); u = 248m b) A = A 1 + A 2 + A 3 = 8m · 11m + 8m · 7m + 8m · 21m = 88m 2 + 56m 2 + 168m 2 = 312m 2 ; A = 312m 2 ; u = 98m 882 a) A = 23,2 cm 2 (23,16) b) u = 284 cm 907 vgl. Dreieck neben Aufg. 886 908 a) u = 15,9 cm; A = 10,0 cm 2 (10,027…) b) u = 30,3m; A = 39,1m 2 (39,097…) 909 a) b = 12,5m b) h c = 10,5 cm 910 a) A = 6m 2 ; u = 12m b) b = 14 cm 911 a) u = 118m (117,6); A = 467m 2 (467,31…) b) u = 113m; A = 356m 2 (356,14…) 912 A = 13,8m 2 ; 342,24 € 913 A = 5,76m 2 ; 6,91m 2 (6,912) 945 kreuze an: A, B und D 946 a 2 + b 2 + c 2 ; c = ​ √ _____ a 2 + b 2​ , a = ​ √ _____ c 2 − b 2​ , b = ​ √ _____ c 2 − a 2​ 947 a) ja b) nein 948 h = 3,0m (3,0049…) 949 l = 1 592m (1 591,50…) (Hinweis: Die Seilbahn benötigt für die Berg- und Talfahrt jeweils ein Drahtseil.) 950 A = 17,9m 2 (17,92); a = 6,99m (6,9856…); u = 19,6m (19,571…) 951 A = 249m 2 (249,41…); h = 20,8m (20,784…) 977 1Ab, 2Ca, 3Bd, 4Dc 978 a) u = 26,2 cm; A = 25,5 cm 2 b) u = 3,6 dm; A = 0,99 dm 2 979 a) u = 152mm; A = 11,0 cm 2 (11,02) b) a = 32,3 dm (32,310…); u = 129 dm (129,24…); A = 720 dm 2 980 u = 41,0 cm (41,01); A = 90 cm 2 981 a) u = 22,2m (22,16); A = 20m 2 b) u = 172m; A = 14,9 a (14,94) 982 a) a = 12,9 dm (12,85) b) a = 23,8mm; h = 5,2mm c) c = 5,04m (5,0384…) d) f = 88m 992 a) A = A 1 + A 2 ; A 1 = 32 cm 2 ; A 2 = 16 cm 2 ; A = 48 cm 2 b) A = A 1 + A 2 ; A 1 = 3 cm 2 ; A 2 = 2,63 cm 2 (2,625); A = 5,63 cm 2 (5,625) 993 Konstruktion: α = 109°, β = 68°, ​ ___  BD​= 10 cm; A = A 1 + A 2 ; A 1 = 11,2 cm 2 (11,204…); A 2 = 17,5 cm 2 (17,457…); A = 28,7 cm 2 (28,661…) 994 a) u = 25,4m (25,36) b) u = 40m 995 a) 1m š 0,5mm; ​ __  AB​= 58mm, ​ __  BC​= 22mm …, α = 52°, β = 95° b) h 1 = 26,5mm š 53m; h 2 = 22,5mm š 45m; h 3 = 19mm š 38m; A 1 = 24 a (24,38), A 2 = 20,7a; A 3 = 22,2 a (22,23); A = 67,3 a (67,31) 996 a) ​ __  AB​= 18,0m (18,027…); ​ __  BC​= 30,9m (30,923…); ​ __  CD​= 26,6m (26,575…); ​ __  DE​= 29,4m (29,364…); ​ __  EF​= 27,6m (27,554…); ​ __  FA​= 32,4m (32,449…); u = 165m (164,894…); A I = 2,43 a; A II = 6,55 a (6,5475); A III = 2,15 a; A IV = 0,75 a; A V = 4,13 a (4,125); A VI = 1,75 a; A = 17,8 a (17,7525) 255 Lösungen Kompetenzcheck Nur zu Prüfzwecken – Eigentum des Verlags öbv