from a handpicked tutor in LIVE 1-to-1 classes

# 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

**☛ Related Questions:**

- A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 13.16).
- A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
- A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3of iron has approximately 8 g mass. (Use π = 3.14)
- A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

visual curriculum