Question

A housing society consisting of 5500 people needs 100l of water per person per day.The cylindrical supply tank is 7m high and has a diameter 10m .For how many days will the water in the tank last for the society.

Answer 1

$\underline{\underline{\bold{Solution:}}}$

Given that, the height (h) of the tank is 7 m and the diameter of its base is 10 m

So, its radius of the tank's circular base ( r ) be

= $\frac{10}{2}$ m

= 5 m

Now, the volume of the tank ( i.e., the capacity of the tank to store water ) is

= π * r² * h

= π * 5² * 7 m³

= 175π m³

= 175π * 1000 litres

= 175000π litres

= 175000 * 3.14 litres ( π = 3.14 )

= 549500 litres

Here, the daily requirements of water is

= 5500 * 100 litres

= 550000 litres

Hence, the tank will last for

= $\dfrac{\text{capacity of tank}}{\text{daily requirements of water}}$

= $\dfrac{549500}{550000}$ days

= 0.999 days

i.e., at most a day