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
Ili kupata urefu wa kontena, tutatumia formula ya eneo la jumla la uso wa kontena bila kifuniko. Step 1: Tambua vipimo vya kontena na uandike formula ya eneo la uso. Kontena ni mstatili (cuboid) na vipimo vifuatavyo: • Upana (w) = 3 cm • Kimo (h) = 6 cm • Urefu (l) = y cm (tunahitaji kupata hii) Kwa kuwa kontena haina kifuniko, ina nyuso 5: chini, mbele, nyuma, na pande mbili. Eneo la chini = l × w = y × 3 = 3y cm^2 Eneo la mbele na nyuma = 2 × (l × h) = 2 × (y × 6) = 12y cm^2 Eneo la pande mbili = 2 × (w × h) = 2 × (3 × 6) = 2 × 18 = 36 cm^2 Jumla ya eneo la uso (Total Surface Area, TSA) = Eneo la chini + Eneo la mbele na nyuma + Eneo la pande mbili. TSA = 3y + 12y + 36 TSA = 15y + 36 Step 2: Tumia eneo la jumla la uso lililopewa na utatue kwa y. Tunapewa kuwa jumla ya eneo la uso ni 111 cm^2. 111 = 15y + 36 Step 3: Tatua mlinganyo ili kupata thamani ya y. Toa 36 kutoka pande zote mbili za mlinganyo: 111 - 36 = 15y 75 = 15y Gawanya pande zote mbili kwa 15: y = (75)/(15) y = 5 Kwa hiyo, urefu wa kontena ni 5 cm. Jibu la mwisho ni: 5\, cm Drop the next question.