# 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:**

Let's visualize the shape of Gulab jamun as shown below.

From the above figure, we can see that,

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

Also,

Diameter of Gulab jamun = diameter of the cylindrical part

Radius of cylindrical part = radius of hemispherical part

In order to find the volume of sugar syrup in 45 Gulab jamuns, we need to find the volume of all the gulab jamun.

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 the volume of 45 gulab jamuns.

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 one Gulab jamun = volume of cylindrical part + 2 × volume of the hemispherical parts

= πr^{2}h + 2 × 2/3 πr^{3}

= πr^{2}h + 4/3 πr^{3}

= πr^{2} (h + 4r/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 × (12.2/3 cm)]

= 75.152/3 cm^{3}

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

= 45 × 75.152/3 cm^{3}

= 15 × 75.152 cm^{3}

= 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).

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 13

**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 (see Fig. 13.15)

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 Question 3

**Summary:**

A gulab jamun, contains sugar syrup up to about 30% of its volume. Approximately 338 cm^{3} 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

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