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A gulab jamun, contains sugar syrup up to about 30% of its volume.find approximately how much syrup would be found is 45 gulab jamun , each shaped like a cylinder with two hemispheriCal ends with length 5 cm and diameter 2.8 cm . |
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Answer» -step EXPLANATION:Each gulab jamun is given the form of a cylinder with two HEMISPHERICAL ends.Diameter of the cylinder = 2.8 CMRADIUS of the cylinder = Diameter of cylinder/2Diameter of the hemisphere = 2.8 cmRadius of the hemisphere = Diameter of hemisphere/2Radius of the hemisphere (r) = 2.8 /2r = 1.4 cmHeight of the cylinder + 2 ✕ Radius of the hemisphere = 5 cmHeight of the cylinder = 5 – (2 ✕ Radius of the hemisphere)Height of the cylinder = 5 – (2 ✕ 1.4)Height of the cylinder (h) = 2.2 cmVolume of Cylinder = πr2hVolume of cylinder = (22/7) ✕ (1.4)2 ✕ 2.2Volume of cylinder = 13.552 cm3Volume of hemisphere = (2/3) πr3Volume of hemisphere = (2/3) ✕ (22/7) ✕ (1.4)3Volume of hemisphere = 0.667 ✕ 3.143 ✕ 2.744Volume of hemisphere = 5.75 cm3NowVolume of two hemisphere = 2 ✕ 5.75 cm3Volume of two hemisphere = 11.5 cm3Let us calculate the volume of the gulab jamunVolume of gulab jamun = Volume of the cylinder + Volume of two hemisphereVolume of gulab jamun = 13.552 cm3 + 11.5 cm3Volume of gulab jamun = 25.052 cm3The volume of one gulab jamun is 25.052 cm3∴ The volume of 45 gulab jamun = 25.052 cm3 ✕ 45The volume of 45 gulab jamun = 1127.34 cm3In gulab jamun quantity of sugar syrup = 30% = 30/100 = 0.3The quantity of sugar syrup in 45 gulab jamun = 0.3 ✕ volume of one gulab jamun ✕ 45The quantity of sugar syrup in 45 gulab jamun = 0.3 ✕ 25.052 ✕ 45The quantity of sugar syrup in 45 gulab jamun = 338.25 cm3. |
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