Water is flowing at the rate of 3 , km/h thro | vedclass

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(B) $1$. Calculate the volume of the cistern: The cistern is cylindrical with radius $r = 5 \, m$ and height $h = 2 \, m$. Volume $V = \pi r^2 h = \pi

Vedclass · Accepted Answer

$1 \, hour \, 40 \, minutes$

Vedclass · Answer

(B) $1$. Calculate the volume of the cistern: The cistern is cylindrical with radius $r = 5 \, m$ and height $h = 2 \, m$. Volume $V = \pi r^2 h = \pi 	imes (5)^2 	imes 2 = 50\pi \, m^3$.$2$. Calculate the volume of water flowing through the pipe per hour: The pipe has radius $r_p = 10 \, cm = 0.1 \, m$. The speed of water is $3 \, km/h = 3000 \, m/h$. The volume of water flowing per hour is $V_p = \pi r_p^2 	imes 	ext{speed} = \pi 	imes (0.1)^2 	imes 3000 = \pi 	imes 0.01 	imes 3000 = 30\pi \, m^3/h$.$3$. Calculate the time required: Time = $\frac{	ext{Volume of cistern}}{	ext{Volume of water per hour}} = \frac{50\pi}{30\pi} = \frac{5}{3} \, hours$.$4$. Convert to hours and minutes: $\frac{5}{3} \, hours = 1 \, hour + \frac{2}{3} 	imes 60 \, minutes = 1 \, hour \, 40 \, minutes$.

Water is flowing at the rate of $3 \, km/h$ through a circular pipe of $20 \, cm$ internal diameter into a circular cistern of diameter $10 \, m$ and depth $2 \, m$. In how much time will the cistern be filled?

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