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). t can be observed that Radius (r) of cylindrical part = Radius (r) of hemispherical part = 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 Volume of 45 gulab jamuns == 1,127.25 cm3 Volume of sugar syrup = 30% of volume plz tell me why it is voulume of gulab jamun is taken to find the sugar suyrup. why we can't take area of gulab jamun in the place volume because container contain gulab jamun we can take their area and then the volume of container. im not able to understand the question. please try to explain with proper diagram.

Answer 1

Length of cylinder = 5 – 2.8 = 2.2 cm, radius = 1.4 cm

Volume of cylinder

Volume of two hemispheres

Total volume

Volume of syrup = 30% of total volume

Volume of syrup in 45 gulabjamuns = 45 x 7.515 = 338.184 cm3

Answer 2

Diameter of the cylindrical part of the gulab jamun = 2.8 cm
Radius = 1.4 cm
Volume of the cylindrical part = πr²h
= 22/7 x 1.4 x 1.4
= 6.16 cm³
Volume of the hemispherical part = 2/3 πr³
= 2/3 x 22/7 x 1.4 x 1.4 x 1.4
= 5.75 cm³
volume of both the hemisperical parts = 5.75 x 2 = 11.5 cm³
total volume of each gulab jamun = 6.16 + 11.5 = 17.66 cm³
volume of 45 gulab jamuns = 17.66 x 45 = 794.7 cm³
sugar syrup = 30% of 794.7
= 794.7 x 30/100
∴ 238.41 cm³