Question

PLZZZ SOLVE THIS QSTN.. ITS FROM MENSURATION... CLASS 10 ICSE ​

Answer 1

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

$\bf{Given\begin{cases}\sf{The\:cylindrical\:tank\:of\:diameter\;(d)\:=\:1.4m}\\ \sf{Radius\:of\:tank\:(r)\:=\cancel{\frac{1.4}{2}} \:=0.7m}\\ \sf{The\:cylindrical\:tank\:of\:height\:(h)\:=\:2.1m}\\ \sf{Diameter\:of\:pipe\:flow\:water\:(d)\:=\:3.5cm}\\ \sf{Radius\:of\:pipe\:(r)\:=\:\frac{3.5}{2} cm}\\ \sf{Water\:flow\:at\:the\:rate\:of\:2m/s.}\end{cases}}$

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The time taken the tank will be filled.

$\bf{\Large{\boxed{\sf{\red{Explanation\::}}}}}}$

We know that formula of the volume of cylinder:

$\leadsto\sf{Volume\:=\:\pi r^{2} h}$

• $\sf{\large{\boxed{\rm{\pink{Volume\:of\:tank\::}}}}}$

$\longmapsto\sf{Volume\:=\:\pi r^{2} h}$

$\longmapsto\sf{Volume\:=\:(\frac{22}{7} *0.7*0.7*2.1)m^{3} }$

$\longmapsto\sf{Volume\:=\:(\frac{22}{\cancel{7}} *\cancel{0.7}*0.7*2.1)m^{3} }$

$\longmapsto\sf{Volume\:=\:(22*0.1*0.7*2.1)m^{3} }$

$\longmapsto\sf{\blue{Volume\:=\:3.234m^{3} }}$

• $\sf{\large{\boxed{\rm{\pink{Volume\:of\:pipe\::}}}}}$

Converts into metre so,

$\longmapsto\sf{Volume\:=\:\pi r^{2} h}$

$\longmapsto\sf{Volume\:=\:(\frac{22}{7} *\frac{3.5}{200}*\frac{3.5}{200} *2)m^{3} }$

$\longmapsto\sf{Volume\:=\:(\frac{22}{7} *\frac{3.5}{200}*\frac{3.5}{\cancel{200}} *\cancel{2})m^{3} }$

$\longmapsto\sf{Volume\:=\:(\frac{22}{7} *\frac{3.5}{200} *\frac{3.5}{100} )m^{3} }$

$\longmapsto\sf{Volume\:=\cancel{\frac{269.5}{140000}} m^{3} }$

$\longmapsto\sf{\blue{Volume\:=\:0.001925m^{3}} }$

Now,

→ Time = $\sf{\frac{Volume\:of\:tank}{Volume\:of\:pipe} }$

→ Time = $\sf{\cancel{\frac{3.234m^{3} }{0.001925m^{3}} } }$

→ Time = 1680m/seconds.

If we converts minutes, then;

$\mapsto\sf{\cancel{\frac{1680}{60} }}$

$\mapsto\sf{28\:minutes}$

Thus,

$\bf{\large{\boxed{\sf{The\:time\:taken\:the\:tank\:will\:be\:filled\:are\:28\:minutes.}}}}}}}$