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

Radius of each hemispherical part , r= `(2.8 )/(2) cm = 1.4 cm `

Radius of the cylindrical part, r= 1.4 cm
Length of the cylindrical part , h = ( 5- 2xx 1.4 ) cm = 2.2 cm
Volume of one gulabjamun
= volume of 2 hemispherical parts + volume of cylinder part
`= (2xx 2/3 pir^3 + pi r^2 h ) (4/3 pi r^3 + pi r^2 h )`
`=pi r^2(4/3 r+ h )= [ 22/7 xx 1.4 xx 1.4 xx (4/3 xx 1.4 + 2.2 )] cm^2`
`= ( 6.16 xx (12.2)/(3))cm^3 = ((75.152)/(3))cm^3`
Volume of 45 gulabjamuns
`= ((75.152)/(3)xx 45)) cm^3 = 1127.28 cm ^3`
Volume of the syrup = ( 30 % of 1127.28) `cm^3`
`=(30/100 xx 1127 . 28 )cm^3 = 338.184 cm^3`
Hence , 45 gulab jamuns contain approximately `338 cm^3` of syrup .