Question

18. The total surface area of a cylinder of height 8 cm is 528 cm². Find the radius of the
base of the cylinder.
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Answer 1

Answer:

$\setlength{\unitlength}{1.5 cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,0.6)(2,0)\qbezier(0,0)( 1, - 0.6)(2,0) \put(2.3,1){\vector(0,1){1.5}}\put(2.3,1){\vector(0, - 1){1.2}}\put(2.5,1){ \bf 8 \: cm }\put(0.4,0.1){ \bf r \: cm }\put(0,0){\vector(1,0){1}}\qbezier(0,2.5)(1,1.9)(2,2.5)\qbezier(0,2.5)(1,3.1)(2,2.5)\end{picture}$

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• Total surface area of cylinder = 528 cm²
• Height of cylinder = 8 cm

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☯ Let Radius of the base of cylinder be r cm.

⠀⠀

$\underline{\bigstar\:\textsf{According to the Question\::}}$

$:\implies\sf 2 \pi r(h + r) = 528$

$:\implies\sf 2 \times \dfrac{22}{7} \times r(8 + r) = 528$

$:\implies\sf \dfrac{44}{7} \times r(8 + r) = 528$

$:\implies\sf r(8 + r) = \cancel{528} \times \dfrac{7}{ \cancel{44}}$

$:\implies\sf 8r + r^2 = 12 \times 7$

$:\implies\sf 8r + r^2 = 84$

$:\implies\sf r^2 + 8r - 84 = 0$

$:\implies\sf r^2 - 6r + 14r - 84 = 0$

$:\implies\sf r(r - 6) + 14(r - 6) = 0$

$:\implies\sf (r - 6)(r + 14) = 0$

$:\implies\sf (r - 6) = 0\quad or \quad(r + 14) = 0$

$:\implies\sf r = 6 \quad or \quad r = - 14$

We know that, radius of a cylinder can't be negative.

⠀⠀

$\therefore\;{\underline{\textsf{Hence,\;Radius\;of\;cylinder\;is\; \textbf{6 cm}.}}}$

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$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:CSA =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area \: of \: Base + CSA + area \: of \: top \\{\quad\:\:\quad=\pi r^2 + 2\pi rh+\pi r^2 = 2 \pi r(h + r)}\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$