Question

the circmfearence of a base of a cylinder is 176cm and its hight is 60 cm find the volume of cylinder

•Don't spam​

Answer 1

$\sf Given \begin{cases} & \sf{Circumference\:of\:base\:of\:cylinder = \bf{176\:cm}} \\ & \sf{Height\:of\:cylinder = \bf{60\:cm}} \end{cases}$

To find: Volume of cylinder?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Circumference_{\;(circle)} = 2 \pi r}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 176\\ \\ \\ :\implies\sf \dfrac{44}{7} \times r = 176\\ \\ \\ :\implies\sf r = \cancel{176} \times \dfrac{7}{ \cancel{44}}\\ \\ \\ :\implies\sf r = 4 \times 7\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{r = 28\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Radius\:of\:cylinder\:is\: {\textsf{\textbf{28\:cm}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\dag\;{\underline{\frak{Now,\:Finding\:Volume\:of\:cylinder,}}}$

⋆ Volume of cylinder is given by,

$\star\;{\boxed{\sf{\pink{Volume_{\;(cylinder)} = \pi r^2 h}}}}$

$:\implies\sf Volume_{\;(cylinder)} = \dfrac{22}{7} \times 28 \times 28 \times 60\\ \\ \\ :\implies\sf Volume_{\;(cylinder)} = \dfrac{22}{ \cancel{7}} \times \cancel{28} \times 28 \times 60\\ \\ \\ :\implies\sf Volume_{\;(cylinder)} = 22 \times 4 \times 28 \times 60\\ \\ \\ :\implies\sf Volume_{\;(cylinder)} = 88 \times 1680\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{Volume_{\;(cylinder)} = 147840\:cm^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Volume\:of\:cylinder\:is\: \bf{147840\:cm^2}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$