Question

find the surface area of the following cylinders radius 3.5 cm and hight 14.9 cm I want all steps and division too​

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• Base radius of a cylinder = 3.5 cm
• Height of the cylinder = 14.9 cm

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The TSA of the cylinder.

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{TSA}_{[Cylinder]}=2\pi r(h+r)\:sq.units}}}$

${\underline{\underline{\bf{Solution:}}}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎We are given with the measures of base radius and height of a cylinder. The TSA of the cylinder has to be found. We can find it by inserting the given measures in the formula of TSA of cylinder:

$\mapsto{\sf{2\pi r(h+r)\:sq.units}}$

The value of $\sf{\pi}$ can be taken as $\sf{\frac{22}{7}}$. Let us do it!

$\:\:\:\:\:\:\:\:\implies{\sf{2\times \dfrac{22}{7}\times 3.5\times (14.9+3.5)}}$

$\:\:\:\:\:\:\:\:\implies{\sf{2\times \dfrac{22}{7}\times 3.5\times 18.4}}$

$\:\:\:\:\:\:\:\:\implies{\sf{2\times \dfrac{22}{\cancel{7}}\times \dfrac{\cancel{35}}{10}\times \dfrac{184}{10}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{2\times 22\times \dfrac{\cancel{5}}{\cancel{10}}\times \dfrac{184}{10}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\cancel{2}\times 22\times \dfrac{1}{\cancel{2}}\times \dfrac{184}{10}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\cancel{22}\times \dfrac{184}{\cancel{10}}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\dfrac{11\times 184}{5}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\dfrac{\cancel{2024}}{\cancel{5}}}}$

$\:\:\:\:\:\:\:\:\implies{\frak{\red{\underline{\underline{404.8\:{cm}^{2}}}}}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• The surface area of the cylinder is 404.8 cm².

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${\underline{\underline{\bf{Some\:related\: formulae:}}}}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:{TSA}_{[Cylinder]}=2\pi r(h+r)\:sq.units}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:{CSA}_{[Cylinder]}=2\pi rh\:sq.units}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:{Volume}_{[Cone]}=\dfrac{1}{3}\pi r^2h\:cu.units}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:{TSA}_{[Cone]}=\pi r(l+r)\:sq.units}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:{CSA}_{[Cone]}=\pi rl\:sq.units}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:{Volume}_{[Sphere]}=\dfrac{4}{3}\pi{r}^{3}\:cu.units}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:{TSA}_{[Sphere]}=4\pi r^2\:sq.units}$

Answer 2

Correct Question-:

• Find the surface area of the cylinder whose Radius is 3.5 cm and height 14.9 cm.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:of\:of\:Cylinder\:  \: = \: 404.8cm^{2} }}}}}$

Explanation-:

$\frak{Given\:\: -:} \begin{cases} \sf{The\:Radius \:of\:Cylinder \:\:is\:= \frak{3.5cm}} & \\\\ \sf{The\:Height \:of\:Cylinder \:is \:=\:\frak{14.9cm}} \end{cases}$

$\frak{To\:Find\:\: -:} \begin{cases} \sf{The\:Total\: Surface \: Area \:of\:Cylinder \:\:} \end{cases}$

Solution-:

$\underline{\dag{\star{\sf{\red{ Total\:Surface\:Area\:of\:Cylinder  \: }}}}}$

• $\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:_{(Cylinder)}  \: = \: 2 × \pi × Radius ( Height+ Radius) }}}}}$

$\frak{Here\:\: -:} \begin{cases} \sf{The\:Radius \:of\:Cylinder \:\:is\:= \frak{3.5cm}} & \\\\ \sf{The\:Height \:of\:Cylinder \:is \:=\:\frak{14.9cm}} & \\\\ \sf{\pi = \frac{22}{7}} \end{cases}$

Now ,

• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × \frac {22}{7} × 3.5 ×( 3.5+14.9)}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × \frac {22}{7} × 3.5 ×18.4}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × \frac {22}{7} × \frac{35}{10} ×18.4}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × 22 × \frac{5}{10} ×18.4}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × 22 × \frac{1}{2} ×18.4}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × 22 × 9.2}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 44 ×9.2}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 404.8cm^{2}}}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:_{(Cylinder)}  \: = \: 404.8cm^{2} }}}}}$

Hence ,

• $\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:of\:of\:Cylinder\:  \: = \: 404.8cm^{2} }}}}}$

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♤More To Know ♤

• $\underline{\boxed{\star{\sf{\blue{ Curved\:Surface\:Area\:_{(Cylinder)}  \: = \: 2 × \pi × Radius × Height }}}}}$
• $\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:_{(Cylinder)}  \: = \: 2 × \pi × Radius ( Height+ Radius) }}}}}$

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