Question

Find the height of the cylinder whose volume is 1.54m³ and diameter of the base is 14cm.​

Answer 1

$\frak{Given}\begin{cases}\sf \:\:Volume\:of\:the\: cylinder=\bf{ 1.54\:m^3} \\ \sf \:\:Diameter\:of\:base\:of\:the\:cylinder=\bf{ 14\:cm }\\ \sf \:\:Radius\:of\:the\: cylinder=\dfrac{D}{2}=\cancel{\dfrac{14}{2}}=7\:cm=\bf {0.07\:m}\end{cases}$

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Need to find: Height of the cylinder.

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$\underline{\bf{\dag}\frak{\:As\:we\:know\:that\::}}$

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$\star\:{\boxed{\pink{\sf{Volume\:_{(cylinder)}=\pi r^2h}}}}$

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where,

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• r & h are the radius and height of the cylinder respectively. And volume of the cylinder is given that is 1.54m³. Now, comparing,

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$:\implies\sf{1.54=\dfrac{22}{7}\times (0.07)^2 \times h}\\\\\\:\implies\sf{1.54=\dfrac{22}{7}\times 0.0049\times h}\\\\\\:\implies\sf{1.54=0.0154\times h}\\\\\\:\implies\sf{h=\dfrac{1.54}{0.0154}}\\\\\\:\implies{\underline{\boxed{\purple{\frak{h=100\:m}}}}}{\:\bigstar}$

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$\therefore{\underline{\sf{\:Hence,\:the\:height\:of\:the\:cylinder\:is\:{\textsf{\textbf{100\:m}}}}.}}$