# 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)

**Solution:**

In Fig. 13.15 visualize the shape of Gulab jamun.

From the above figure, we can see that,

Length of cylindrical part = length of a Gulab jamun - 2 x radius of the hemispherical part

Also,

Diameter of Gulab jamun = diameter of cylindrical part

Radius of cylindrical part = radius of hemispherical part

In order to find the volume of sugar syrup in 45 Gulab jamun we find volume of Gulab jamun.

Using the statement:

The volume of the solid formed by joining 2 basic solids will actually be sum of the volumes of its constituents.

Volume of 1 Gulab jamun = volume of cylindrical part + volume of the 2 hemispherical parts

As it’s given a Gulab jamun contains sugar syrup up to about 30% of its volume. We make an assumption to every Gulab jamun contains sugar syrup at 30% of its volume to simplify the calculation.

Volume of sugar syrup = 30% of volume of 45 Gulab jamun.

Diameter of the Gulab jamun, d = 2.8 cm

Radius of cylindrical part = radius of hemispherical part r = d/2 = 2.8/2 cm = 1.4 cm

Length of cylindrical part, h = 5 cm - 2 × 1.4 cm = 2.2 cm

Volume of 1 Gulab jamun = volume of cylindrical part + 2 x volume of the hemispherical parts

= πr^{2}h + 2 × 2/3 πr^{3}

= πr^{2}h + 4/3 πr^{3}

= [22/7 × 1.4 cm × 1.4 cm × (2.2 cm + 4/3 × 1.4 cm)

= [22/7 × 1.4 cm × 1.4 cm × (122.2/3 cm)]

= 75.152/3 cm^{3}

Volume of 45 Gulab jamuns = 45 × volume of 1 Gulab jamun

= 45 × 75.152/3 cm^{3}

= 15 × 75.152 cm³

= 1127.28 cm^{3}

Volume of sugar syrup in 45 Gulab jamuns = 30% of volume of 45 Gulab jamun

= 30/100 × 1127.28 cm^{3}

= 338.184 cm^{3}

Thus, the volume of sugar syrup in 45 cylindrical-shaped Gulab jamuns is 338 cm^{3} (approximately)

**Video Solution:**

## 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

### NCERT Solutions Class 10 Maths - Chapter 13 Exercise 13.2 Question 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

The volume of sugar syrup in 45 cylindrical-shaped Gulab jamuns with two hemispherical ends is 338 cm^{3}