Four pipes each of 5 cm in diameter are to be replaced by a single pipe discharging the same quantity of water. If the speed of water remains same in both the cases, then the diameter (in cm) of the single pipe is

5

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10

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Solution

The correct option is C $10$
Radius of four pipes $= 2.5 c m$
Radius of single pipe $= R$
If all the pipes are of length $l$
Volume of the pipe $= π r^{2} l$
Thus, Volume of water from four pipes $=$ Volume of water from a single pipe
$4 π (2.5)^{2} l = π R^{2} l$
$\Rightarrow R^{2} = 25 {c m}^{2}$
$\Rightarrow R = 5 c m$
Diameter $= 10 c m$

Hence, option 'C' is correct.

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Four pipes each of 5 cm in diameter are to be replaced by a single pipe discharging the same quantity of water. If the speed of water remains same in both the cases, then the diameter (in cm) of the single pipe is

The correct option is C 10Radius of four pipes =2.5 cmRadius of single pipe =RIf all the pipes are of length lVolume of the pipe =πr2lThus, Volume of water from four pipes =Volume of water from a single pipe4π(2.5)2l=πR2l⇒R2=25 cm2⇒R=5 cmDiameter =10 cmHence, option 'C' is correct.