Water flows at the rate of 10 , m/min through | vedclass

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Question

(A) Given,speed of water flow $= 10 \, m/min = 1000 \, cm/min$.Radius of the pipe $r = \frac{5 \, mm}{2} = 2.5 \, mm = 0.25 \, cm$.Area of the cross-s

Vedclass · Accepted Answer

$51 \, min \, 12 \, s$

Vedclass · Answer

(A) Given,speed of water flow $= 10 \, m/min = 1000 \, cm/min$.Radius of the pipe $r = \frac{5 \, mm}{2} = 2.5 \, mm = 0.25 \, cm$.Area of the cross-section of the pipe $= \pi r^2 = \pi 	imes (0.25)^2 = 0.0625 \pi \, cm^2$.Volume of water flowing per minute $= 	ext{Area} 	imes 	ext{Speed} = 0.0625 \pi 	imes 1000 = 62.5 \pi \, cm^3$.Volume of the conical vessel $= \frac{1}{3} \pi R^2 H$,where $R = 20 \, cm$ and $H = 24 \, cm$.Volume $= \frac{1}{3} \pi 	imes (20)^2 	imes 24 = 8 \pi 	imes 400 = 3200 \pi \, cm^3$.Time required $= \frac{	ext{Volume of vessel}}{	ext{Volume per minute}} = \frac{3200 \pi}{62.5 \pi} = \frac{3200}{62.5} = 51.2 \, minutes$.$51.2 \, minutes = 51 \, minutes + 0.2 	imes 60 \, seconds = 51 \, minutes \, 12 \, seconds$.

Water flows at the rate of $10 \, m/min$ through a cylindrical pipe $5 \, mm$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40 \, cm$ and depth $24 \, cm$?

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