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A school provides milk to the student daily in cylindrical glasses of diameter 7 cm. If the glass is filled with milk up to the height of 12 cm, find how many litres of milk is needed to serve 1600 students. Use $\pi = \dfrac{{22}}{7}$.

Last updated date: 15th Jul 2024
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Hint- This is a very simple question which only we should be aware of three things which are first, they should know the volume of the cylinder, then one also should know the use of basic operations like multiplication and division which can get complicated at some part but it will become simple as we move on. Then we should also know about $1000{\text{ c}}{{\text{m}}^3} = 1{\text{ litre}}$ this will help you to know about the amount in litres once solved in $c{m^3}$. By these simple three things you will know about the solution.

Complete step-by-step answer:
Radius of cylindrical glass =$3.5cm$
Height up to the glass filled with milk = 12 cm
Volume of cylindrical glass = $\pi {r^2}h$
  \dfrac{{22}}{7} \times 3.5 \times 3.5 \times 12 \\
   = \dfrac{{3234}}{7} \\
   = 462{\text{ c}}{{\text{m}}^3} \\
Volume of 1 cylindrical glass = $462{\text{ }}c{m^3}$
Volume of 1600 cylindrical glass $ = 1600 \times 462$
$ = 739200{\text{ c}}{{\text{m}}^3}$
  1000{\text{ c}}{{\text{m}}^3} = 1{\text{ litre}} \\
  {\text{739200 c}}{{\text{m}}^3} = 739.2{\text{ liters}} \\
Therefore, $739.2{\text{ liters}}$of milk is needed to serve 1600 students.

Note- In this question it should be noted that what is the volume of the cylinder this will allow you to solve most of the question but one must be sure of his calculation otherwise, the whole question can be wrong. Some normal calculations tips like trying to solve parts will make the solution easy and calculations simpler. Also one must know that $1000{\text{ c}}{{\text{m}}^3} = 1{\text{ litre}}$ this will help you to solve the question and find answer in litres. Thus by these simple rules you should be able to solve the question.