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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2. The circumference of a circle is 187cm. Calculate its diameter. Step 1: Tumia fomula ya mzingo wa duara, C = d. Tunapewa C = 187 cm. Tutatumia = (22)/(7). 187 = (22)/(7) × d Step 2: Ili kupata kipenyo d, zidisha pande zote mbili kwa (7)/(22). d = 187 × (7)/(22) Step 3: Rahisisha hesabu. d = (187 × 7)/(22) d = (1309)/(22) d = 59.5 cm Kipenyo cha duara ni 59.5 cm. 3. A wheel has a diameter of 70cm. How many meters will it cover after making 300 revolutions? Step 1: Kwanza, tafuta mzingo (circumference) wa gurudumu. Mzingo ni umbali unaofunikwa kwa mzunguko mmoja. Tumia fomula C = d. Tutatumia = (22)/(7). C = (22)/(7) × 70 cm C = 22 × 10 cm C = 220 cm Step 2: Tafuta jumla ya umbali uliosafiri baada ya mizunguko 300. Jumla ya umbali = C × idadi ya mizunguko Jumla ya umbali = 220 cm × 300 Jumla ya umbali = 66000 cm Step 3: Badilisha umbali kutoka sentimita kwenda mita. Tunajua kuwa 1 m = 100 cm. Jumla ya umbali (mita) = (66000)/(100) m Jumla ya umbali (mita) = 660 m Gurudumu litafunika umbali wa 660 m. 4. A circular field has a radius of 60m. An athlete ran round the field four times. What distance in km did he cover? (=3.142) Step 1: Kwanza, tafuta mzingo (circumference) wa uwanja wa duara. Mzingo ni umbali wa mzunguko mmoja. Tumia fomula C = 2 r. C = 2 × 3.142 × 60 m C = 6.284 × 60 m C = 377.04 m Step 2: Tafuta jumla ya umbali aliosafiri mwanariadha baada ya kuzunguka uwanja mara nne. Jumla ya umbali = C × 4 Jumla ya umbali = 377.04 m × 4 Jumla ya umbali = 1508.16 m Step 3: Badilisha umbali kutoka mita kwenda kilomita. Tunajua kuwa 1 km = 1000 m. Jumla ya umbali (km) = (1508.16)/(1000) km Jumla ya umbali (km) = 1.50816 km Mwanariadha alifunika umbali wa 1.50816 km. Tuma swali linalofuata 📸