Question

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:

• A. 5
• B. 6
• C. 10
• D. 12

Answer 1

The correct option is A

5

Four pipes each of 5cm in diameter
$\Rightarrow$ radius r =2.5 cm
Let the height be h.
Volume of small pipe =$\pi r^{2}h$
(since we are considering the height (length) of the pipe as constant or same)
Let the height be h
Volume of new pipe = Sum of volumes of all small pipes
$\pi R^{2}h=4\times \pi \times (2.5{)}^2\times h$
$R^2=4\times (2.5{)}^2$
$R=2\times \left(2.5\right)=5cm$