Question

Find the weight of a solid cylinder of radius 10.5 cm and height 60 cm, if the material of the cylinder weighs 5 grams per cm³.​

Answer 1

$\frak{Given}\begin{cases}\sf{Radius\;of\;the\;solid\;cylinder=\bf{10.5\;cm}}\\\sf{Height\;of\;the\;solid\;cylinder=\bf{60\;cm}}\\\sf{Weight\;of\;material\;of\;the\;cylinder=\bf{5\;g/cm^3}}\end{cases}$

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Need to find: The weight of the solid cylinder.

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

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$\star\:{\boxed{\pink{\sf{Volume_{(cylinder)}=πr^2h}}}}$

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Where,

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• r & h are radius and height of the cylinder respectively.

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$:\implies{\sf{Volume_{(cylinder)}=\bigg(\dfrac{22}{7}×10.5×10.5×60\bigg)\:cm^3}}\\\\\\:\implies{\sf{Volume_{(cylinder)}=20790\;cm^3}}$

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Now,

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Weight of 1 cm³ = 5 g

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$\therefore\sf{Weight_{(cylinder)}=(20790×5)\;g}\\\\\\:\implies\sf{Weight_{(cylinder)}=103950\;g}\\\\\\:\implies\sf{Weight_{(cylinder)}=\cfrac{103950}{1000}\;kg}\\\\\\:\implies{\underline{\boxed{\purple{\sf{Weight_{(cylinder)}={\frak{103.95\;{\sf{kg}}}}}}}}}{\;\bigstar}$

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$\sf{\underline{Hence,\;the\;weight\;of\;the\;solid\;cylinder\;is\;{\bf{103.95\;kg}}.}}$