A school provides milk to the students daily in cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto a height of 12 cm, find how many litres of milk is needed to serve 1600 students.

Given diameter = 7 cm, height = 12 cm.

We know,

radius = $\dfrac{\text{diameter}}{2} = \dfrac{7}{2} = 3.5$ cm.

Volume of cylinder = πr²h.

Putting values we get,

$\text{Volume of milk in 1 glass } = \dfrac{22}{7} \times (3.5)^2 \times 12 \\[1em] = \dfrac{22 \times 12.25 \times 12}{7} \\[1em] = \dfrac{3234}{7} \\[1em] = 462 \text{ cm}^3.$

∴ Volume of milk in 1600 glasses = 1600 × 462 = 739200 cm³.

Since 1000 cm³ = 1 litre so, 1 cm³ = $\dfrac{1}{1000}$ litre.

So, Volume of milk in 1600 glasses = $739200 \times \dfrac{1}{1000}$ litres = 739.2 litres.

Hence, 739.2 litres of milk is required for serving 1600 students.