A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup should be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with a length of 5 cm and a diameter of 2.8 cm as shown in the below figure.
A cylinder shape in mathematics is a three-dimensional solid figure which consists of two circular bases connected with two parallel lines.
Answer: The quantity of sugar syrup in 45 gulab jamuns will be 338.202 cm3.
A hemisphere is a three-dimensional shape that is half of the sphere. When a sphere is cut by a plane passing through its center, the shape we get is called the hemisphere. The volume of a hemisphere of some radius can be easily found out by calculating just half of the volume of a sphere of the same radius.
The diameter of the cylinder = 2.8 cm
Thus, the radius = Diameter/2
= 1.4 cm
Radius of the hemisphere = Radius of the cylinder = 1.4 cm
Height of the cylinder + 2 × Radius of the hemisphere = 5 cm
Height of the cylinder + Diameter of the hemisphere = 5 cm
Thus, height of the cylinder = 5 – diameter of the hemisphere
Height of the cylinder = 5 – 2.8
Height of the cylinder (h) = 2.2 cm
Now, we will calculate the volume of the hemisphere by using the formula (2/3) πr3
The volume of hemisphere = (2/3) × (22/7) × (1.4)3
= 5.75 cm3
Since there are two hemispheres present in one Gulab jamun,
The volume of two hemispheres = 2 × 5.75 cm3
= 11.5 cm3
Now, we will calculate the Volume of the Cylinder by using the formula πr2h
Volume of cylinder = (22/7) × (1.4)2 × 2.2
= 13.552 cm3
Let's calculate the volume of the gulab jamun by adding the volume of the cylinder and the volume of the two hemispheres.
The volume of gulab jamun = Volume of the cylinder + Volume of two hemispheres
Volume of gulab jamun = 13.552 cm3 + 11.5 cm3
= 25.052 cm3
∴ The volume of 45 gulab jamun = 45 × 25.052 cm3
= 1127.34 cm3
In one gulab jamun, the quantity of the sugar syrup = 30% × Volume of gulab jamun
The quantity of sugar syrup in 45 gulab jamuns = 30% × Volume of 45 gulab jamuns
= 0.3 × 1127.34 cm3
= 338.202 cm3
The quantity of sugar syrup in 45 gulab jamuns = 338.202 cm3