Q. 34.0( 452 Votes )

A gulabjamun contains sugar syrup up to about30% of its volume. Find approximately how much syrup would be found in 45 gulabjamun each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see Fig. 13.15)


Answer :



Radius (r) of cylindrical part == 1.4 cm
Radius (R) of hemispherical part == 1.4 cm

Length of each hemispherical part = 1.4 cm

The radius of hemispherical part = 1.4 cm

Length (h) of cylindrical part = 5 - 2 × Length of hemispherical part

= 5 -( 2 × 1.4 )
= 5 - 2.8

= 2.2 cm

The volume of one gulabjamun = Vol. of cylindrical part + 2 × Vol. of hemispherical part

= (πr2h )+ (2 × πR3)

= (πr2h) + (R3)

= [π × (1.4)2 × 2.2] +[  (1.4)3]

=

= 13.552 + 11.498

= 25.05 cm3

Volume of 45 gulabjamun = 45 × 25.05

= 1,127.25 cm3

The volume of sugar syrup = 30% of the volume

= × 1127.25

= 338.17 cm3

= 338 cm3(approx)

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