A Gulab Jamun when completely ready for eating contains sugar syrup up to about 30 % of its volume. Find approximately how much syrup would be found in 45 Gulab Jamun shaped like a cylinder with two hemispherical ends if the complete length of each of the Gulab Jamun is 5 cm and its diameter is 2.8 cm.

To solve this problem, we need to find the volume of the syrup in 45 Gulab Jamuns.

### Step 1: Volume of one Gulab Jamun
Each Gulab Jamun is shaped like a cylinder with two hemispherical ends. We can calculate the volume of one Gulab Jamun by adding the volume of the cylinder and the volumes of the two hemispherical ends.

#### Volume of the cylinder
The formula for the volume of a cylinder is:
\[ V_{\text{cylinder}} = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

The diameter of each Gulab Jamun is 2.8 cm, so the radius \( r = \frac{2.8}{2} = 1.4 \) cm. The length of the Gulab Jamun is 5 cm, and since the ends are hemispherical, the length of the cylindrical part is reduced by twice the radius (for both hemispherical ends). Therefore, the height of the cylindrical part is:
\[ h = 5 - 2 \times 1.4 = 5 - 2.8 = 2.2 \, \text{cm} \]

Now, we can calculate the volume of the cylinder:
\[ V_{\text{cylinder}} = \pi (1.4)^2 (2.2) = \pi \times 1.96 \times 2.2 \approx 13.55 \, \text{cm}^3 \]

#### Volume of the two hemispherical ends
The volume of one hemisphere is given by the formula:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \]
The total volume of the two hemispheres is:
\[ V_{\text{hemispheres}} = 2 \times \frac{2}{3} \pi r^3 = \frac{4}{3} \pi r^3 \]
Substituting \( r = 1.4 \) cm:
\[ V_{\text{hemispheres}} = \frac{4}{3} \pi (1.4)^3 = \frac{4}{3} \pi \times 2.744 = 11.51 \, \text{cm}^3 \]

#### Total volume of one Gulab Jamun
Now, we can find the total volume of one Gulab Jamun by adding the volume of the cylindrical part and the volume of the two hemispherical ends:
\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemispheres}} = 13.55 + 11.51 = 25.06 \, \text{cm}^3 \]

### Step 2: Volume of syrup in one Gulab Jamun
We are told that the Gulab Jamun contains sugar syrup up to 30% of its volume. Therefore, the volume of syrup in one Gulab Jamun is:
\[ V_{\text{syrup}} = 0.30 \times 25.06 = 7.52 \, \text{cm}^3 \]

### Step 3: Volume of syrup in 45 Gulab Jamuns
Now, to find the total volume of syrup in 45 Gulab Jamuns, we multiply the volume of syrup in one Gulab Jamun by 45:
\[ V_{\text{total syrup}} = 45 \times 7.52 = 338.4 \, \text{cm}^3 \]

### Final Answer:
The total volume of syrup in 45 Gulab Jamuns is approximately 338.4 cm³.