A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

Explanation

Let r be the radius of the hemisphere and cylinder both , `h_(1)` be the height of the himishpere which is equal to its radius and `h_(2)` be the height of the cylinder .Given length =5 cm diameter =2.8 cm
`r=h_(1)=(2.8)/(2)=1.4 cm`
`h_(2)=PQ-(PR+SQ)`
=5-1.4+1.4
=5-2.8=2.2 cm
Volume of one gulab jamun=2`xx`(volume of hemisphere)+ volume of cylinder
`2xx(2)/(3)pir^(3)+pir^(2)h_(2)=(4)/(3)pir^(3)`
`pir(2)((4r)/(3)+h^(2))=(22)/(7)xx1.4xxx1.4((4)/(3)xx1.4+22)`
`(22)/(7)xx(14)/(10)xx(14)/(10)(4)/(3)xx(14)/(10)+(22)/(10)=(9394)/(375)=(9394)/(375)cm^(3)`
volume of 45 gulab jamuns `=45xx(9394)/(375)=1127.28 cm^(3)`
Hence , quantity of syrup found in 45 gulab jamuns
`=1127.28xx(30)/(100)`
=338.184=338 `cm^(3)`