Question

A solid cylinder of height 9m has its curved surface area equal to one third
of the total surface area. What is the radius of the base?​

Answer 1

GiVen:-

• Height =9 m

To Find:-

• Radius of the base of cylinder.

AnSwer:-

$\sf \: Curved \: surface \: area : \\ \sf \: = 1/3 × total \: surface \: area.$

$\sf \: Curved \: surface \: of \: the \: solid \: cylinder \: \\ \sf \: = \: 2πrh$

$\sf \: Total \: surface \: area : \\ \sf \: =2\pi {r}^{2} + 2\pi rh$

Therefore,

$\\ \implies \sf \: 2\pi rh = \dfrac{1}{3} (2\pi {r}^{2} + 2\pi rh ) \\ \\ \implies \sf \: 6\pi rh = 2\pi {r}^{2} + 2\pi rh \\ \\ \implies \sf \: 4\pi rh = 2\pi {r}^{2} \\ \\ \implies \sf \:r = 2h \\ \\ \implies \sf \:r = 2 \times 9 \\ \\ \implies { \underline{ \boxed{ \pink{\sf {\:r = 18 \: m}}}}}$

Answer 2

$\sf{\huge{\mathfrak{\pink{\underline{Question}}}}}$

• A solid cylinder of height 9m has its curved surface area equal to one third of the total surface area. What is the radius of the base?

$\sf{\huge{\mathfrak{\pink{\underline{solution</p><p>n}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• height of cylinder = 9m
• CSA = 1/3 TSA

$\sf{\bold{\blue{\underline{\underline{To\: Find }}}}}$

• radius of cylinder = ???

$\sf{\bold{\purple{\underline{\underline{Answer}}}}}$

$\sf{\bold{\red{\boxed{CSA = 2\pi r h }}}}$

$\sf{\bold{\red{\boxed{TSA = 2 \pi r^2 + 2\pi r h }}}}$

$\sf \implies 2\pi r h = \dfrac{1}{3}(2 \pi r^2 + 2\pi r h )$

$\sf \implies 6 \pi r h = 2\pi r^2 + 2 \pi r h$

$\sf \implies 6 \pi r h - 2 \pi r h = 2 \pi r^2$

$\sf \implies 4 \pi r h = 2 \pi r^2$

$\sf\implies \dfrac{\cancel{4 \pi r h }}{\cancel{2 \pi r^2}} = 1$

$\sf\implies 2h = r$

$\sf\implies r = 2 \times 9$

$\sf\implies r = 18m$

$\sf{\bold{\orange{\boxed{radius = 18m}}}}$

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