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.
ScanSolve AI Answer
Huu hapa ni ukokotozi wa ujazo wa gimba: Step 1: Tambua thamani zilizotolewa na kokotoa urefu wa koni. Rediasi ya hemisifia na koni, r = 3.5 cm. Jumla ya urefu wa gimba, H = 12 cm. Thamani ya = (22)/(7). Urefu wa hemisifia ni sawa na rediasi yake, yaani 3.5 cm. Urefu wa koni (h_koni) utakuwa jumla ya urefu kutoa urefu wa hemisifia: h_koni = H - r = 12 cm - 3.5 cm = 8.5 cm Step 2: Kokotoa ujazo wa hemisifia (V_hemisifia). Fomula ya ujazo wa hemisifia ni (2)/(3) r^3. V_hemisifia = (2)/(3) × (22)/(7) × (3.5)^3 V_hemisifia = (2)/(3) × (22)/(7) × 42.875 V_hemisifia = (1886.5)/(21) V_hemisifia ≈ 89.833 cm^3 Step 3: Kokotoa ujazo wa koni (V_koni). Fomula ya ujazo wa koni ni (1)/(3) r^2 h_koni. V_koni = (1)/(3) × (22)/(7) × (3.5)^2 × 8.5 V_koni = (1)/(3) × (22)/(7) × 12.25 × 8.5 V_koni = (2289.25)/(21) V_koni ≈ 109.012 cm^3 Step 4: Kokotoa ujazo jumla wa gimba (V_jumla). Ujazo jumla ni jumla ya ujazo wa hemisifia na ujazo wa koni. V_jumla = V_hemisifia + V_koni V_jumla = 89.833 cm^3 + 109.012 cm^3 V_jumla = 198.845 cm^3 Kwa kutumia sehemu kamili kwa usahihi zaidi: V_hemisifia = (539)/(6) cm^3 V_koni = (1309)/(12) cm^3 V_jumla = (539)/(6) + (1309)/(12) = (1078)/(12) + (1309)/(12) = (2387)/(12) cm^3 V_jumla ≈ 198.917 cm^3 Ujazo wa gimba ni: 198.917 cm^3 Tuma swali linalofuata 📸