Question

Solve the following equations: (1) A gulab jamun contains sugar syrup up to about 30% of its volume.
(a) Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5cm and diameter 2.8cm

Answer 1

Hint: Try to start the question by listing down what is given to us and what we have to find out. Next, you can calculate the volume of the entire cylinder by separately calculating volume of cylinder and volume of two hemispheres. Adding this we get our total volume and then find the percentage.

Complete step-by-step solution:
Let's start the solution with listing down what is given to us: the gulab jamun is a cylinder with two hemispherical ends.
Also, length = 5cm and diameter = $2.8 cm$ and gulab jamun contains syrup up to 30%
Let us first try to find the volume of one gulab jamun.
Total length given is 5cm.
So the length of the cylinder=total length-radius of top hemisphere- radius of bottom hemisphere
Since diameter = 2radius
We get our radius as 1.4cm.
Therefore length of cylinder= $5-1.4-1.4 = 2.2cm$
Now volume of gulab jamun =volume of the cylinder +volume of the two hemispheres
Total volume= $3\pi {r^2}\pi h + 2\left( {\dfrac{2}{3}\pi {r^3}} \right)$
Substituting the known values we get
Volume=
$ = \left( {\dfrac{{22}}{7} \times {{\left( {1.4} \right)}^2}} \right)\left( {\left( {3 \times 2.2} \right) + \left( {\dfrac{4}{3} \times 1.4} \right)} \right)$
$
   = \dfrac{{75.152}}{3} \\
   = 25.05{\text{c}}{{\text{m}}^3} \\
 $
This is the volume of one gulab jamun.
Since we have been given 45 gulab jamuns, their total volume will be $45 \times 25.05 = 1127.2830{\text{c}}{{\text{m}}^3}$
Also we have been told that the gulab jamun contains 30% syrup
Therefore the percentage of syrup in 45 gulab jamun will be
$ = 1127.2830 \times \dfrac{{30}}{{100}}$
$ = 338.184{\text{c}}{{\text{m}}^3}$

Hence, $338.184{\text{c}}{{\text{m}}^3}$syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5cm and diameter 2.8cm.

Note: In this kind of question try to always start the solution with what is given to us and what we have to find. This makes us clear about our aim. After this try not to jump to find the final step but start with the basic steps first which will build further to our final step. Each and every step should be written with precise formulas used.