#### Question

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 (see the given figure). Use [Π = 22/7]

#### Solution

It can be observed that

Radius (*r*) of cylindrical part = Radius (*r*) of hemispherical part = 2.8/2 = 1.4 cm

Length of each hemispherical part = Radius of hemispherical part = 1.4 cm

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

= 5 − 2 × 1.4 = 2.2 cm

Volume of one gulab jamun = Vol. of cylindrical part + 2 × Vol. of hemispherical part

= pir^2h+2xx2/3pir^3 = pir^2h+ 4/3pir^3

= pixx(1.4)^2 xx 2.2 + 4/3pi (1.4)^2

=22/7 xx 1.4 xx 1.4xx2.2+4/3xx22/7xx1.4xx1.4xx1.4

=13.552+11.498 = 25.05 cm^{3}

Volume of 45 gulab jamuns = 45 x25.05= 1,127.25 cm^{3}

It can be observed that

Radius (*r*) of cylindrical part = Radius (*r*) of hemispherical part = 2.8/2 = 1.4 cm

Length of each hemispherical part = Radius of hemispherical part = 1.4 cm

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

= 5 − 2 × 1.4 = 2.2 cm

Volume of one gulab jamun = Vol. of cylindrical part + 2 × Vol. of hemispherical part

`= pir^2h+2xx2/3pir^3 = pir^2h+ 4/3pir^3`

`= pixx(1.4)^2 xx 2.2 + 4/3pi (1.4)^3`

`=22/7 xx 1.4 xx 1.4xx2.2+4/3xx22/7xx1.4xx1.4xx1.4`

=13.552+11.498 = 25.05 cm^{3}

Volume of 45 gulab jamuns = 45 x 25.05 = 1,127.25 cm^{3}

Volume of sugar syrup = 30% of volume

= 30/100 x 1127.25

= 338.17 cm^{3}

= 338 cm^{3}