Question

Hemisphere tank Full of water empty by pipe at the rate of 5 liters per second. How much time will it take to empty half the tank, if it is 3m in diameter?

Answer 1

Given,

Hemisphere tank full of water empty by pipe at the rate of $5$ liters per second.

if it is $3m$ in diameter.

Volume of the tank $=\frac{2}{3} \pi r^{3}$

$=\frac{2}{3}\times\frac{22}{7}\times\frac{3}{2}^{2}$

$=\frac{2}{3}\times\frac{22}{7}\times\frac{27}{8} \\=\frac{99000}{14}$

Volume of water to be empty $=\frac{1}{2}\times$volume of tank

$=\frac{1}{2}\times\frac{99000}{14}$

$=\frac{99000}{28}$

Time taken to empty $5$ liters $=1$ sec

Time taken to empty $1$ liter $= \frac{1}{5}$ sec

Time taken to empty $\frac{99000}{28}$ liters $= \frac{1}{5}\times\frac{99000}{28}$

$=707.14$sec

Therefore, $707.14$ sec take to empty half the tank.

Answer 2

Given,

Hemisphere tank which contains full of water.

It can make empty by a pipe at the rate of $5 lit/sec$

The diameter of the tank is $3m$

Volume of water which has to make empty to half

$=\frac{2}{3} \pi r^{3}/2$

Radius=Diameter/2

$\frac{3}{2} \\=1.5m$

$V=\frac{\frac{2}{3}\pi r^{3} }{2}$

$V=\frac{\frac{2}{3}\times 3.14\times (1.5)^{3} }{2}$

$V=\frac{3.14\times 3.37 }{3}$

$V=\frac{10.5975}{3}$

$V=3.5357$

$V=3535.7$

Time taken to empty $5 lit$

We have to find for $1lit=\frac{1}{5} sec$

Time taken to empty $3535.7lit$

$=3535.7\times \frac{1}{5}$

$=707.14sec$

Therefore, time taken to empty is $707.14sec$