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 Irene, twende na swali la kwanza la "MONDAY". 1. The figure below represents a cylindrical piece of wood of a diameter 35 cm and length 100 cm. Determine the surface area of the wood. (Take = (22)/(7)) Kielelezo kinaonyesha nusu-silinda. Eneo lote la uso wa nusu-silinda linajumuisha: • Nusu ya eneo la uso uliopinda wa silinda kamili. • Nusu-duara mbili (ambazo huunda duara moja kamili). • Msingi wa mstatili. Kutoka kwa swali: Kipenyo (D) = 35 cm Urefu (L) = 100 cm Radiasi (r) = (D)/(2) = (35)/(2) cm = (22)/(7) Step 1: Kokotoa eneo la uso uliopinda wa nusu-silinda. Eneo la uso uliopinda wa nusu-silinda = r L r L = (22)/(7) × (35)/(2) cm × 100 cm = (11 × 5) × 100 cm^2 = 55 × 100 cm^2 = 5500 cm^2 Step 2: Kokotoa eneo la nusu-duara mbili (ambazo huunda duara moja kamili). Eneo la duara moja kamili = r^2 r^2 = (22)/(7) × ((35)/(2))^2 cm^2 = (22)/(7) × (35)/(2) × (35)/(2) cm^2 = 11 × 5 × (35)/(2) cm^2 = 55 × (35)/(2) cm^2 = (1925)/(2) cm^2 = 962.5 cm^2 Step 3: Kokotoa eneo la msingi wa mstatili. Eneo la msingi = D × L D × L = 35 cm × 100 cm = 3500 cm^2 Step 4: Jumlisha maeneo yote kupata eneo lote la uso wa mbao. Eneo lote la uso = Eneo la uso uliopinda + Eneo la nusu-duara mbili + Eneo la msingi TSA = 5500 cm^2 + 962.5 cm^2 + 3500 cm^2 TSA = 9962.5 cm^2 3 done, 2 left today. You're making progress.