Question

Water comes out of a pipe at a speed of 5 m per second. If the radius of the pipe is
8 cm, find the volume of water (in liters) that can be discharged by the pipe in 5
minutes. (Take pi = 3.14).​

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{3014400 \ litres \ of \ water \ can \ be \ discharged}$

$\sf{in \ 5 \ minutes \ through \ the \ pipe.}$

$\sf\orange{Given:}$

$\sf{For \ cylindrical \ pipe,}$

$\sf{\implies{Radius (r)=8 \ cm=0.08 \ m}}$

$\sf{\implies{Speed \ of \ water=5 \ m \ s^{-1}}}$

$\sf{\implies{Time(t)=5 \ minutes=300 \ seconds}}$

$\sf\pink{To \ find:}$

$\sf{The \ volume \ of \ water \ discharged.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\boxed{\sf{Distance=Time\times \ Speed}}$

$\sf{\therefore{Distance=300\times5}}$

$\sf{\therefore{Distance=1500 \ m}}$

$\sf{But, \ here \ distance=height \ of \ cylindrical \ pipe.}$

$\sf{\therefore{Height \ of \ cylindrical \ pipe=1500 \ m}}$

$\boxed{\sf{Volume \ of \ cylinder=\pi\times \ r^{2}\times \ h}}$

$\sf{\therefore{Volume \ of \ cylindrical \ pipe=\pi\times0.08^{2}\times1500}}$

$\sf{\therefore{Volume \ of \ cylindrical \ pipe=3.14\times64\times15}}$

$\sf{\therefore{Volume \ of \ cylindrical \ pipe=3014.4 \ m^{3}}}$

$\sf{\therefore{The \ volume \ of \ water \ discharged=3014.4 \ m^{3}}}$

$\sf{But, 1 \ m^{3}=1000 \ litres.}$

$\sf{\therefore{The \ volume \ of \ water \ discharged=3014.4\times1000 \ litres}}$

$\sf{\therefore{The \ volume \ of \ water \ discharged=3014400 \ litres}}$

$\sf\purple{\tt{\therefore{3014400 \ litres \ of \ water \ can \ be \ discharged}}}$

$\sf\purple{\tt{in \ 5 \ minutes \ through \ the \ pipe.}}$

Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{Water \ comes \ out \ of \ pipe \ at \ a \ speed \ of}$

$\rm{5 \ ms^{1}. \ If \ the \ radius \ of \ the \ pipe \ is \ 8 \ cm,}$

$\rm{Find \ the \ volume \ of \ water \ ( \ in \ liters \ ) \ that }$

$\rm{can \ be \ discharged \ by \ the \ pipe \ in \ 5 \ min.}$

$\rm{( \ Take \ pi =3.14 ) .}$

____________________________________________

$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\tt{\blue{\underline{\red{3014400 \ litres \ of \ water \ can \ be \ discharged}}}}$

$\tt{\blue{\underline{\red{in \ 5 \ minutes \ through \ the \ pipe.}}}}$

____________________________________________

$\sf\large\underline\pink{Given:}$

$\rm{For \ cylindrical \ pipe,}$

$\rm{Radius (r)=8 \ cm=0.08 \ m}$

$\rm{Speed \ of \ water=5 \ m \ s^{-1}}$

$\rm{Time(t)=5 \ minutes=300 \ seconds}$

____________________________________________

$\sf\large\underline\blue{To \ Find}$

$\sf{The \ volume \ of \ water \ discharged.}$

____________________________________________

$\green{\underline{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}}$

$\rm{We \ know}$

$\star{\rm{Distance=Time\times \ Speed}}$

$\rm{\implies{Distance=300\times5}}$

$\rm{\implies{Distance=1500 \ m}}$

$\rm{But, \ in \ this \ case ,}$

$\rm{Distance \ is \ equal \ to \ the \ height \ of \ the \ cylinder}$

$\rm\therefore{distance \ = \ Height \ of \ cylinder}$

$\rm{\therefore{Height \ of \ cylindrical \ pipe=1500 \ m}}$

$\rm{Also,}$

$\star{\rm{Volume \ of \ cylinder}}$

$\rm{\implies{ \pi\times \ r^{2}\times \ h}}$

$\rm{\therefore{Volume \ of \ cylindrical \ pipe}}$

$\rm{\implies{ \pi\times0.08^{2}\times1500}}$

$\rm{\therefore{Volume \ of \ cylindrical \ pipe}}$

$\rm{\implies{3.14\times64\times15}}$

$\rm{\therefore{Volume \ of \ cylindrical \ pipe}}$

$\rm{\implies{3014.4 \ m^{3}}}$

$\rm{\therefore{The \ volume \ of \ water \ discharged}}$

$\rm{\implies{3014.4 \ m^{3}}}$

$\rm{\therefore{The \ volume \ of \ water \ discharged}}$

$\rm{\implies{3014.4\times1000 \ litres}}$

$\rm{As, 1 \ m^{3}=1000 \ litres.}$

$\rm{\therefore{The \ volume \ of \ water \ discharged}}$

$\rm{\implies{3014400 \ litres}}$

$\tt{\blue{\underline{\red{3014400 \ litres \ of \ water \ can \ be \ discharged}}}}$

$\tt{\blue{\underline{\red{in \ 5 \ minutes \ through \ the \ pipe.}}}}$

___________________________________________

$\rm\red{Hope \ it \ helps \ :))}$