Question

A water tank is hemispherical below and cylindrical at the top. If the radius is 12 m and capacity is 3312π cubic metre, the height of the cylindrical portion in metres is:

Answer 1

${ \large{ \sf{ \underbrace{\underline{\bigstar \: Answer}}}}}$

$\tt{Volume\: of\: a \:cylinder}[tex]\small{=\: πr^2h \: cubic \: metre}$

$\sf\color{green}{= (144π x h)}$$\bold{cubic\: metre}$

$\textit{Volume\: of \:a\: hemisphere}$

$\sf\color{gold}{= 2/3πr^2h \:cubic \:metre}$

$\sf\color{gold}{=\: (144π x 8) cubic\: metre}$

$\bold{Volume\: of \:the \:water \:tank}$

$\sf\color{maroon}{= (πr^2h + 2/3πr^2h) cubic units }$

$\sf\color{maroon}{= 144π (8 + h) cubic metre}$

$\sf\bold\color{red}{According\: to \:the \:question,}$

$\tt{We\: have}$

$\sf\color{blue}{144π (8 + h) = 3312π}$

$\sf\color{blue}{(8 + h) = 23 or h = (23 - 8) metre}$

$\small\color{red}{= \:15\: metre}$

$\large{So,}$

$\small\color{purple}{the\: height \:of\: the \:cylinder \:is \:15 \:metre.}$

Thankyou :)