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

Hint: We first find the dimensions of a Gulab jamun and its volume. Then we find the syrup volume in a particular Gulab jamun. We also find the total volume for 45 such Gulab jamuns.

Complete step-by-step solution:
Gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter $2.8$ cm. The radius will be half of the diameter which is $\dfrac{2.8}{2}=1.4$ cm.

From the given dimensions of the Gulab jamuns we can find their volume.
We know that the volume for a cylindrical shape with base radius $r$ and height $h$ is $\pi {{r}^{2}}h$.
Therefore, the volume of a Gulab jamun is $\pi {{r}^{2}}h=\dfrac{22\times {{1.4}^{2}}\times 5}{7}=30.8c{{m}^{3}}$.
Now we know that one Gulab jamun contains sugar syrup up to about 30% of its volume.
So, one Gulab jamun has syrup of volume $\dfrac{30.8\times 30}{100}=9.24c{{m}^{3}}$.
We have 45 such Gulab jamuns which gives the total syrup volume as $9.24\times 45=415.8c{{m}^{3}}$.
The volume of syrup in those Gulab jamuns is $415.8c{{m}^{3}}$.

Note: We can also convert the volume to our known forms of unit of litre where we know that $1000c{{m}^{3}}$ is equal to 1 litre. So, we get $415.8c{{m}^{3}}=\dfrac{415.8}{1000}=0.4158$ litre.