48 3. 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 Fig. 13.15).
Answers
Given parameters:
- Each gulab jamun is given the form of a cylinder with two hemispherical ends.
Diameter of the cylinder = 2.8 cm
⠀
Radius of the cylinder = Diameter of cylinder/2
⠀
Diameter of the hemisphere = 2.8 cm
⠀
Radius of the hemisphere = Diameter of hemisphere/2
⠀
Radius of the hemisphere (r) = 2.8 /2
r = 1.4 cm
⠀
Height of the cylinder + 2 ✕ Radius of the hemisphere = 5 cm
Height of the cylinder = 5 – (2 ✕ Radius of the hemisphere)
Height of the cylinder = 5 – (2 ✕ 1.4)
Height of the cylinder (h) = 2.2 cm
⠀⠀ ⠀
⠀
Volume of Cylinder = πr²h
Volume of cylinder = (22/7) ✕ (1.4)2 ✕ 2.2
Volume of cylinder = 13.552 cm³
⠀
Volume of hemisphere = (2/3) πr³
Volume of hemisphere = (2/3) ✕ (22/7) ✕ (1.4)³
Volume of hemisphere = 0.667 ✕ 3.143 ✕ 2.744
Volume of hemisphere = 5.75 cm³
⠀
Now
Volume of two hemisphere = 2 ✕ 5.75 cm³
Volume of two hemisphere = 11.5 cm³
⠀
⠀
Let us calculate the volume of the gulab jamun
Volume of gulab jamun = Volume of the cylinder + Volume of two hemisphere
Volume of gulab jamun = 13.552 cm³ + 11.5 cm³
Volume of gulab jamun = 25.052 cm³
The volume of one gulab jamun is 25.052 cm³
⠀
⠀
∴ The volume of 45 gulab jamun = 25.052 cm³ ✕ 45
The volume of 45 gulab jamun = 1127.34 cm³
⠀
In gulab jamun quantity of sugar syrup = 30% = 30/100 = 0.3
⠀
The quantity of sugar syrup in 45 gulab jamun = 0.3 ✕ volume of one gulab jamun ✕ 45
⠀
The quantity of sugar syrup in 45 gulab jamun = 0.3 ✕ 25.052 ✕ 45
The quantity of sugar syrup in 45 gulab jamun = 338.25 cm³