Question

Water flows through a cylindrical pipe of diameter 7cm. at 36km/hr. Calculate time in minutes it would take to fill a cylindrical tank of radius 35 cm and height 1m.



with proper working

Answer 1

36km/hr = 10m/s
volume of water flowing through the pipe in one second is
$\pi \times {0.035}^{2} \times 10$
where 0.035 is the radius of pipe in metre

volume of the cylindrical tank is
$\pi \times (0.35)^{2} \times 1$
therefore time taken to fill the tank in seconds is
$\frac{\pi \times 0.35 \times 0.35}{\pi \times 0.035 \times 0.035 \times 10}$
that is 10 seconds
1/6 minutes

Answer 2

Radius of pipe = 7/2cm

Rate of water flow = 36 km/h

= 36 xx 5/18 m/s

= 10 m/s

= 10 x 100 cm/s.

= 1000 cm/s

Volume of water flowing in 1 second = πr²h

= π×7/2×7/2×1000cm³

= π x 7 x 7 x 250 cm3 ....(1)

Radius of tank (R) = 35 cm

Height of tank (H) = 1 m = 100 cm

∴ Volume of tank = πr2H

= π x 35 x 35 x 100 cm3 ...(2)

∴ Time taken to fill the tank =

$= \frac{Volume \: \: of \: \: tank}{Volume \: of \: \: water \: \: flowing \: \: in \: 1 sec}$

$= \frac{\pi \times 35 \times 35 \times 100}{\pi \times 7 \times 7 \times 250}$

$= 10 \: sec$

$= \frac{10}{60} \: min$

$= \frac{1}{6} \: min$

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