Question

A farmer connects a pipe of internal diameter 25cm from a canal into a cylindrical tank in his field, which is 12m in diameter and 2.5m deep.If water flows through the pipe at the rate of 3.6 km/hr, in how much time will the tank will be filled? Also find the cost of water,if the canal department charges at the rate of Rs 0.07/m3

Answer 1

➡️➡️Answer:

Time taken by pipe to fill the tank is 1.6 hour.

Cost charge by canal department = 19.8 Rs

Solution:
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Pipe(refers as cylinder):

Radius =12.5 cm

if pipe take x hours to fill the tank,so

length(height) = $3.6x \: km$

Water tank(Cylinder):
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Radius = 6 m

Height= 2.5 m

$volume \: of \: water \: tank \: = \pi \: {r}^{2} h \\ \\ = \pi \times 6 \times 6 \times 2.5 \: {m}^{3}$

water flows from pipe = Volume of water tank

$\pi \times 0.125 \times 0.125 \times 3.6 x\times 1000 = \pi \times 6 \times 6 \times 2.5 \\ \\ x = \frac{6 \times 6 \times 2.5}{0.125 \times 0.125 \times 3.6 \times 1000} \\ \\ = \frac{6 \times 6 \times 25 \times 1000000}{125 \times 125 \times 36 \times 1000} \\ \\ = \frac{1000}{5 \times 125} \\ \\ = \frac{40}{5 \times 5} \\ \\ = \frac{8}{5} hour \\ \\ = 1.6 \: hour$

Time taken by pipe to fill the tank is 1.6 hour.

To find the cost of water,if the canal department charges at the rate of Rs 0.07/m3

$= \frac{22}{7} \times 6 \times 6 \times 2.5 \times 0.07 \\ \\ = \frac{22 \times 36 \times 25 \times 7}{7 \times 1000} \\ \\ = \frac{19800}{1000} \\ \\ =19.8 Rs$

Hope it helps you.