Question

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

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?

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

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

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

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

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

⋆ Volume of cylinder is given by,

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

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

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

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

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

Answer 2

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Given :-}}}}}}$

☞ Circumference of base of the cylinder = 176cm

☞ Height of cylinder = 60cm

$\Large{\underline{\underline{\textsf{\maltese\: {\red{To Find :-}}}}}}$

☞ Volume of cylinder = ?

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Recalling the concepts :-}}}}}}$

☞ Circumference of circle = 2πr

☞ Volume of cylinder = πr²h

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Solution :-}}}}}}$

The shape of the base of cylinder is circle so will use the formula to compute the circumference of circle.

☞ Circumference of circle = 2πr

⇒ 2πr = 176cm

⇒ 2 × $\dfrac{22}{7}$ × r = 176cm

⇒ r = 176cm × $\dfrac{7}{22}$ × $\dfrac{1}{2}$

⇒ r = 28cm

∴ Radius of circular base of cylinder = 28cm

Now we find the volume of cylinder.

☞ Volume of cylinder = πr²h

⇒ Volume of cylinder = $\sf{\dfrac{22}{7} \times 28cm \times 28cm \times 60cm }$

⇒Volume of cylinder = 147,840cm³

∴ Volume of cylinder = 147,840cm³.

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Additional Information about cylinder :-}}}}}}$

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

◆ NOTE : Additional Information can also be seen in the attached image.