Answer

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**Hint:**To solve this question, we will use some basic formulae of surface area and volumes of figures. We have to remember that the volume of cylinder with height h and radius r is given by $\pi {r^2}h$ and volume of hemisphere is given by $\dfrac{2}{3}\pi {r^3}$

**Complete step-by-step answer:**

Given that,

Length of Gulab jamun = 5cm.

Diameter of hemispherical ends = 2.8cm.

So,

Radius of hemisphere = $\dfrac{{2.8}}{2} = 1.4cm$

We know that,

Volume of hemisphere = $\dfrac{2}{3}\pi {r^3}$

So, the volume of the hemispherical end of the Gulab jamun will be,

$ \Rightarrow \dfrac{2}{3} \times \dfrac{{22}}{7} \times {\left( {1.4} \right)^3}$

$ \Rightarrow 5.75c{m^3}$

According to the question, there are two hemispherical ends in the Gulab jamun.

So, the total volume of the hemispherical ends = $2 \times $volume of hemispherical end.

$ \Rightarrow 2 \times 5.75c{m^3}$

$ \Rightarrow 11.5c{m^3}$

Here, the height of the cylindrical part of the Gulab jamun will be given as,

$ \Rightarrow $ length of Gulab jamun – ( $2 \times $radius of hemispherical end )

$ \Rightarrow 5 - \left( {2 \times 1.4} \right)$

$ \Rightarrow 5 - \left( {2.8} \right)$

$ \Rightarrow 2.2cm$

We know that, volume of cylinder = $\pi {r^2}h$

So, the volume of the cylindrical part of Gulab jamun is,

$ \Rightarrow \dfrac{{22}}{7} \times {\left( {1.4} \right)^2} \times 2.2$

$ \Rightarrow 13.55c{m^3}$

Therefore, the total volume of the Gulab jamun = volume of cylindrical part + volume of hemispherical part

$ \Rightarrow V = 11.5 + 13.55$

$ \Rightarrow V = 25.05c{m^3}$

According to the question, 30% of the volume of Gulab jamun is the sugar syrup.

So, the volume of sugar syrup in 1 Gulab jamun = $\dfrac{{30}}{{100}} \times V$

$ \Rightarrow \dfrac{{30}}{{100}} \times 25.05c{m^3}$

$ \Rightarrow 7.515c{m^3}$

Therefore,

The sugar syrup in 45 Gulab jamun = $45 \times 7.515c{m^3}$

$ \Rightarrow 338.175c{m^3}$

Hence, we can say that the approximate volume of sugar syrup in 45 Gulab jamuns is $338c{m^3}$

**Note:**In this type of questions, we should know the formula of volume of cylinder and hemisphere. First, we will find out the volume of 1 Gulab jamun by considering the both cylindrical and hemispherical part. Then, we will find the volume of sugar syrup in 1 Gulab jamun by doing 30% of it. After that, we will multiply that volume with 45 and we will get the required volume of sugar syrup.

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