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: Let us draw the figure of gulab jamun and then find the syrup for one gulab jamun. After that we multiply that by 45 to find the syrup in 45 gulab jamuns.

Complete Step-by-Step solution:

As we can see from the above figure that one gulab jamun consists of one cylinder and two hemispheres.
Height of the cylinder is 5 cm and radius of cylinder and hemisphere is \[\dfrac{{2.8}}{2}\] = 1.4 cm
As we know that the volume of a cylinder with height h and radius r is \[\pi {r^2}h\].
And the volume of the hemisphere with radius r is \[\dfrac{{2\pi {r^3}}}{3}\].
As we know that volume of one gulab jamun = volume of cylinder + 2*volume of hemisphere.
So, volume of one gulab jamun will be = \[\pi {\left( {1.4} \right)^2}5\] + 2\[ \times \]\[\dfrac{{2\pi {{\left( {1.4} \right)}^3}}}{3}\]
Volume of one gulab jamun = \[9.8\pi \] + 2\[ \times \]\[1.8293\pi \] = \[13.4586\pi \]\[c{m^3}\]
Now as we know that the syrup in one gulab jamun is 30% of its volume.
And we know that if we have to find A% of B then it may be written as \[\dfrac{A}{{100}} \times B\].
So, applying the percentage formula.
Volume of syrup for one gulab jamun = \[\dfrac{{30}}{{100}} \times 13.4586\pi = 4.03758\pi c{m^3}\].
Now the volume of syrup for 45 gulab jamun will be = \[\left( {4.03758\pi \times 45} \right)c{m^3}\].
As we know that \[\pi = 3.14\]. So,
Volume of syrup found in 45 gulab jamuns will be = \[4.03758 \times 3.14 \times 45 = 570.51{\text{ }}c{m^3}\]
Hence, the volume of syrup found will be \[570.51{\text{ }}c{m^3}\].

Note: Whenever we come up with this type of problem then first, we find the volume of one gulab jamun and then find the volume of syrup in one gulab jamun by applying percentage formula. After that we multiply the volume of syrup in one gulab jamun by 45 to get the total syrup found in 45 gulab jamuns. This will be the easiest and efficient way to find the solution of the problem.