Question

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​

Answer 1

Given:

Volume of gulab jamun = 30%

Length of hemisphere = 5cm.

Diameter of hemisphere = 2.8cm = radius = 1.4cm.

Solution:

Given, h = 5cm.

Length of cylinder, h = 5 - 2.8

⟹ 2.2cm

• Volume of Gulab jamun = Volume of cylinder + volume of 2 hemispheres.

⟹ Volume = 3πr²h + 4/3 πr²

⟹ 22/7 × 1.4 × 1.4 × (3×2.2×4×1.4)/3

⟹ 6.16(12.2)/3

⟹ 75.152/3

⟹ 25.05 cm³

Hence, There are 45 gulab jamuns.

⟹ Volume = 45 × 25.05

⟹ 1127.2830 % of syrup.

Volume = 1127.28 × 30/100

Volume = 338.184 cm³

Hence :

• Volume of syrup will be 338.184 cm³.

Answer 2

Provided Data :

• A Gulab jamun contains sugar syrup up to about 30% of its volume.
• No. of Gulab jamuns, → 45.
• Each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

To Calculate :

• How much syrup would be found in 45 gulab jamuns approximately.

Appropriate Answer :

Here, a gulab jamun is the combination of

• a cylinder , and
• two hemispheres.

⠀⠀⠀⠀⠀Working Rule

We have,

• Diameter of the hemispherical part ⇒ 2.8 cm
• Radius of the hemispherical part

Radius of cylindrical part ⇒ 1.4 cm

Total length of the gulab jamun ⇒ 5 cm

Length of the cylindrical part ⇒ ( L - 2r ) cm

$\sf\longrightarrow \: (5 - 2.8) cm$

$\sf\longrightarrow \:2.2 cm$

Therefore, Volume of one gulab jamun ⇒

( Volume of cylindrical part ) + 2( Volume of hemispherical part )

Formula we are going to use :

Volume of a Cylindrical part :-

⠀⠀$\bf{\underline{V = \pi r^{2}h}}$

Volume of Hemispherical part :-

⠀⠀$\bf{\underline{V = \dfrac{2}{3}\pi r^{3}}}$

$\implies \frac{22}{7} \: \times \: 1.4 \: \times \: 1.4 \: \times \: (2.2 \: + \: \frac{4}{3} \: \times \: 1.4) \: \\ \\ \implies \: \frac{22}{7} \: \times \: \frac{14}{10} \: \times \: \frac{14}{10} \: (2.2 \: + \: \frac{5.6}{3} ) \\ \\ \implies \: 22 \: \times \: \frac{2}{10} \: \times \: \frac{14}{10} \: \times \: \frac{12.2}{3} \: \\ \\ \: \implies \frac{75152}{3 \times 1000} \: \\ \\ \implies 25.05 \: {cm}^{3}$

→ Volume of 45 gulab jamuns → 25.05 × 45 cm³

$\implies$1127.25 cm³

Quantity of sugar - syrup in 45 gulab jamuns

$\implies$ 30 % of 1127.25

$\implies\frac{30}{100} \: \times \: 1127.25 \: {cm}^{3}$

$\sf\longrightarrow \:338.175 {cm}^{3}$

$\implies$338 cm³ ( Approx )

Hence,

The required quantity of sugar syrup in 45 gulab jamuns is 338 cm³ ( approx.)

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