Question

A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of Rs 0.07 per $m^3$.

Answer 1

R = radius of cylinder = 6m

H = height of cylinder = 2.5m

r = radius of pipe = $\frac{25}{2}cm=\frac{1}{8}$m

Rate of flow of water = $\frac{3.6km}{hr}$

In 1 hr water upto a length of 3.6km = 3600m will come out of pipe.

let the tank be filled in 'x' hrs.

volume of water coming out of pipe in x hrs = volume of cylindrical tank.

$\frac{(22}{7}\times \frac{1}{8}\times \frac{1}{8}\times 3600\times \left(x\right)=\frac{22}{7}\times 6\times 6\times 2.5$

$\frac{1}{8}x\frac{1}{8}\times 3600\times x$ = 6 x 6 x 2.5

$3600\times \left(x\right)=36x2.5x8x8$

$100\times =8x8x2.5$

$1000\times \left(x\right)=8x8x25$

$x=\frac{16}{10}=1.6hrs$

$\to x=1hr.36min.$

Now,

$costofwater=volumeofcylindricaltank\times 0.07$

$=22/7x6x6x2.5x0.07$

= Rs.19.80.

The tank will be filled in 1hr.36 min and the cost of water will be Rs.19.80