This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya, hebu tusuluhishe maswali haya hatua kwa hatua. Swali la 5: Kipenyo cha bwawa ni 21 m. Tunahitaji kupata umbali kuzunguka bwawa, ambayo ni mzingo. Mzingo wa duara hutolewa na fomula C = d. Step 1: Andika fomula ya mzingo na badilisha thamani zinazojulikana. C = d C = (22)/(7) × 21\, m Step 2: Rahisisha hesabu. C = 22 × 3\, m C = 66\, m Umbali kuzunguka bwawa ni 66 m. Swali la 6: Mdomo wa baiskeli una rediasi ya 0.7 m. Tunahitaji kujua umbali unaofunikwa katika mizunguko 100. Kwanza, tafuta mzingo wa mdomo (umbali unaofunikwa katika mzunguko mmoja). Mzingo wa duara hutolewa na fomula C = 2 r. Step 1: Andika fomula ya mzingo na badilisha thamani zinazojulikana. C = 2 r C = 2 × (22)/(7) × 0.7\, m Step 2: Rahisisha hesabu ya mzingo. C = 2 × (22)/(7) × (7)/(10)\, m C = 2 × (22)/(10)\, m C = (44)/(10)\, m C = 4.4\, m Step 3: Tafuta umbali wa jumla unaofunikwa katika mizunguko 100. Umbali wa jumla = C × 100 Umbali wa jumla = 4.4\, m × 100 Umbali wa jumla = 440\, m Umbali unaofunikwa katika mizunguko 100 ni 440 m. Swali la 7: Mzingo wa pete ya duara ni 8.8 cm. Tunahitaji kupata rediasi yake. Mzingo wa duara hutolewa na fomula C = 2 r. Step 1: Andika fomula ya mzingo na badilisha thamani zinazojulikana. C = 2 r 8.8\, cm = 2 × (22)/(7) × r Step 2: Rahisisha upande wa kulia wa mlinganyo. 8.8\, cm = (44)/(7) r Step 3: Tatua kwa r kwa kuzidisha pande zote mbili kwa (7)/(44). r = 8.8\, cm × (7)/(44) r = (88)/(10)\, cm × (7)/(44) r = (2)/(10)\, cm × 7 r = (14)/(10)\, cm r = 1.4\, cm Rediasi ya pete ni 1.4 cm. Swali la 1.a (chini ya 3.3 Area): Tafuta eneo la pembetatu iliyoonyeshwa. Eneo la pembetatu hutolewa na fomula A = (1)/(2) × base × height. Step 1: Tambua urefu na msingi wa pembetatu. Msingi = 18 cm Urefu = 10 cm Step 2: Badilisha thamani kwenye fomula na ukokotoe. A = (1)/(2) × 18\, cm × 10\, cm A = 9\, cm × 10\, cm A = 90\, cm^2 Eneo la pembetatu ni 90 cm^2. Swali la 2 (upande wa kulia): Sakafu ya Flora ina urefu wa 12 m na upana wa 8 m. Amefunika sakafu kwa zulia, akiacha ukingo wa 1 m pande zote. Tunahitaji kupata eneo la sakafu ambalo halijafunikwa na zulia. Step 1: Kokotoa eneo la sakafu nzima. Eneo la sakafu = urefu × upana Eneo la sakafu = 12\, m × 8\, m Eneo la sakafu = 96\, m^2 Step 2: Kokotoa vipimo vya zulia. Kwa kuwa kuna ukingo wa 1 m pande zote, urefu na upana wa zulia utapungua kwa 1+1=2 m. Urefu wa zulia = 12\, m - 1\, m - 1\, m = 10\, m Upana wa zulia = 8\, m - 1\, m - 1\, m = 6\, m Step 3: Kokotoa eneo la zulia. Eneo la zulia = urefu wa zulia × upana wa zulia Eneo la zulia = 10\, m × 6\, m Eneo la zulia = 60\, m^2 Step 4: Tafuta eneo la sakafu ambalo halijafunikwa na zulia. Eneo lisilofunikwa = Eneo la sakafu - Eneo la zulia Eneo lisilofunikwa = 96\, m^2 - 60\, m^2 Eneo lisilofunikwa = 36\, m^2 Eneo la sakafu ambalo halijafunikwa na zulia ni 36 m^2. Swali la 3 (upande wa kulia): Tafuta eneo la umbo lililoonyeshwa. Umbo hili lina mstatili na nusu duara. Step 1: Kokotoa eneo la mstatili. Urefu wa mstatili = 14 cm Upana wa mstatili = 10 cm Eneo la mstatili = urefu × upana Eneo la mstatili = 14\, cm × 10\, cm Eneo la mstatili = 140\, cm^2 Step 2: Kokotoa eneo la nusu duara. Kipenyo cha nusu duara ni 10 cm, hivyo rediasi yake ni r = (10)/(2) = 5 cm. Eneo la duara ni r^2, kwa hivyo eneo la nusu duara ni (1)/(2) r^2. Eneo la nusu duara = (1)/(2) × (22)/(7) × (5\, cm)^2 Eneo la nusu duara = (1)/(2) × (22)/(7) × 25\, cm^2 Eneo la nusu duara = (11 × 25)/(7)\, cm^2 Eneo la nusu duara = (275)/(7)\, cm^2 Step 3: Tafuta eneo la jumla la umbo. Eneo la jumla = Eneo la mstatili + Eneo la nusu duara Eneo la jumla = 140\, cm^2 + (275)/(7)\, cm^2 Ili kuongeza, tunahitaji kupata denominator ya kawaida. 140 = (140 × 7)/(7) = (980)/(7) Eneo la jumla = (980)/(7)\, cm^2 + (275)/(7)\, cm^2 Eneo la jumla = (980 + 275)/(7)\, cm^2 Eneo la jumla = (1255)/(7)\, cm^2 Kama desimali (takriban): Eneo la jumla ≈ 179.29\, cm^2 Eneo la umbo ni (1255)/(7) cm^2 au takriban 179.29 cm^2. Tuma swali linalofuata 📸