Question

A hemispherical tank of diameter 3 Meter full of water. It is being empied by a pipe at
the rate of 25/7
litre per second. How much time will it take to make the tank half
empty?
​

Answer 1

ANSWER:-

Given:

A hemispherical tank of diameter 3m full of water. It is being by a pipe at the rate of 25/7 litre/second.

To find:

The time will it take to make the tank half empty.

Explanation:

We have,

A hemispherical tank with their diameter is 3m.

∴ Radius of hemispherical tank= $\frac{3}{2} m$

We know that formula of the volume of hemisphere: 2/3πr³ cubic unit

⇒ Volume of the hemispherical tank= $\frac{2}{3} *\frac{22}{7} *(\frac{3}{2} )^{3}$

⇒ Volume of the hemispherical tank=$(\frac{2}{3}*\frac{22}{7} *\frac{3}{2} *\frac{3}{2} *\frac{3}{2} )m^{3}$

⇒ Volume of the hemispherical tank= $\frac{99}{14} m^{3}$

Therefore,

We know that 1m³ = 1000 litres;

$=\:\frac{99}{14} *1000\\\\=\:\frac{99000}{14} \:l$

Volume of water emptied the half of the volume of hemispherical tank;

$=\:(\frac{1}{2} *\frac{99000}{14} )\:l$

$=\:\frac{99000}{28} \:litres$

Given,

Tank is emptied at 25/7 litres/ second.

⇒ Time taken to empty 25/7 litres= 1 second

⇒ Time taken to empty 1 litres= $1*\frac{7}{25}\:seconds$

⇒ Time taken to empty 99000/28 litres= $\frac{7}{25} *\frac{99000}{28}$

⇒ Time taken to empty 99000/28 litres= $(\frac{693000}{700} )\:seconds$

⇒ Time taken to empty 99000/28 litres= 990 seconds.

We can convert into minutes then;

$=\:\frac{990}{60} \\\\=\:16.5\:minutes$

Thus,

The time taken to make the tank half empty is 16.5 minutes.