Question

total surface area of a cylinder of height 5.5cm is 198cm2 find its radius​

Answer 1

$Let \: r \:and \: h \:are \: radius \:and \:height \\of \: a \: cylinder \: respectively$

$h = 5.5 \:cm$

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

$Total \: Surface\:Area \: of \:the \: cylinder \\= 198 \:cm^{2} \:(given)$

$\implies 2\pi r(r+h) = 198$

$\implies 2 \times \frac{22}{7} \times r(r+5.5)= 198$

$\implies 2r(r + 5.5) = 198 \times \frac{7}{22}$

$\implies 2r^{2} + 11r = 63$

$\implies 2r^{2} + 11r - 63 = 0$

/* Splitting the middle term,we get */

$\implies 2r^{2} + 18r - 7r - 63 = 0$

$\implies 2r( r + 9 ) - 7( r + 9 ) = 0$

$\implies ( r + 9 )( 2r - 7 ) = 0$

$\implies ( r + 9 ) = 0 \: Or \: 2r - 7 = 0$

$\implies r = -9\: Or \: 2r = 7$

$\implies r = -9\: Or \: r = \frac{7}{2}$

/* r should not be negative */

Therefore.,

$\red { Radius \:of \:the \: cylinder }$

$\green { = \frac{7}{2} \:cm = 3.5 \:cm }$

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Answer 2

Answer:

3.5cm

Step-by-step explanation: