A gulab jamun, contains sugar syrup up to about 30% of its volume.

Leave a Comment / Class 10th Case Study, surface areas and volumes / By preeti

Q) 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.

Ans:

STEP BY STEP SOLUTION

Let’s understand the steps to calculate: First, we will calculate the volume of each Gulab Jamun and then volume of sugar syrup will be calculated which is 30% within 45 Gulab Jamuns.

Let’s start from calculating the volume of Gulab Jamun:

Let’s reconstruct the diagram of Gulab Jamun as combination of a cylinder with two hemispheres at both ends.

Let’s calculate dimensions of this cylinder and hemispheres.

Since the diameter of hemisphere is 2.8 cm, hence its radius will be 1.4 cm

Same will also be the radius of the cylinder.

Now, the length of the cylinder = 5 – 2 x 1.4 = 2.2 cm

Let’s calculate volume of each shape one by one:

(i) Volume of cylindrical shape:

We know that the volume of the cylinder = $\pi r^2 h$

Given that the radius of the cylinder is 1.4 cm and height of the cylinder is 2.2 cm

$\therefore$ the volume of the cylinder = $\pi (1.4)^2 (2.2) = 4.31 \pi$

(ii) Volume of 2 Hemispheres:

We know that, Volume of a hemisphere = $\frac{2}{3} \pi r^3$

Hence, the volume of 2 hemispheres = $\frac{4}{3} \pi r^3$

Since, the radius of the hemisphere = 1.4 cm

$\therefore$ the volume of a 2 hemispheres = $\frac{4}{3} \pi (1.4)^3 = 3.66 \pi$

(iii) Total Volume of 45 Gulab Jamuns:

$\because$ the Volume of the Gulab Jamun = Volume of Cylinder + Volume of 2 hemispheres

= $4.31 \pi + 3.66 \pi = 7.97 \pi$

= $7.97 \times \frac{22}{7} = 25.05$ cm³

$\therefore$ the volume of 45 Gulab Jamuns = 45 x 25.05 = 1127.28 cm³

(iv) Volume of Sugar Syrup:

Given that the Sugar Syrup is 30% of the Gulab Jamun’s volume,

$\therefore volume of sugar syrup = 30% x 1127.28 = 338.18 cm³

Therefore, the volume of Sugar Syrup is 338.18 cm³

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