Question

The total surface area of a cylinder whose radius is 1/3 of its height h is

Answer 1

$Let \: height \:of \: a \: cylider = h \:units$

/* According to the problem given */

$Radius \:of \: the \: cylinder (r) = \frac{h}{3} \:units$

$\boxed { \pink { TSA \: of \: a \: Cylinder = 2\pi r( r + h ) }}$

$TSA \: of \: a \: Cylinder \\= 2\pi \times \Big(\frac{h}{3}\Big) [ \frac{h}{3} + h ] \\</p><p>= \frac{2\pi h}{3} [ \frac{h+3h}{3} ] \\= \frac{2\pi h}{3} [ \frac{4h}{3} ] \\= \frac{8}{9} \pi h^{2} \: square \:units$

Therefore.,

$\red { Total \: surface \:area \:of \:the \: Cylinder }\\\green {= \frac{8}{9} \pi h^{2} \: square \:units}$

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