Question

Total surface area of a cylinder of height 5.5cm is 198cm2. Find its radius.

Answer 1

Answer:

$\large{\boxed {\green{3.5}}}$

Step-by-step explanation:

$\large \boxed{ \sf \: given}$

$\sf \: Area \: of \: a \: cylinder = \green{198 {cm}^{2} }$

$\sf \: height = \red{5.5cm }$

$\large{ \boxed{ \sf \: \blue{ Area = 2πr (h + r)}}}$

$\sf198 = 2 \times \frac{22}{7}r (5.5 + r)$

$\sf \: 2r(r+5.5)=198× \frac{22}{7}$

$\sf \implies2r^{2} +11r=63$

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

$\sf \: \implies 2r^{2} +11r \: − \: 63 \: = \: 0$

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

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

Splitting the middle term,we get

$\sf \implies \: 2r^{2} + \: 18r− \: 7r−63 \: = \: 0$

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

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

$\sf \: r=−9 \: \: Or \: \: \frac{7}{2}$

$\sf \: Radius \: = \: \frac{7}{2} = \large{\boxed {\green{3.5}}}$