Question

find the curved surface area and total surface area of a cylinder r = 4.2 cm and h = 14 cm ​

Answer 1

Answer:

• The CSA of the cylinder is and the 369.6 cm² and the TSA of the cylinder is 480.48 cm².

Explanation:

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

• Base radius of a cylinder = 4.2 cm
• Height of the cylinder = 14 cm

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

• The curved surface area and total surface area of the cylinder.

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

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

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

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

$\red\bigstar$ CSA of the cylinder

By inserting the measures of radius and height in the formula:

$\mapsto{\sf{2\pi rh\:sq.units}}$

we can find the CSA of the cylinder. The value of $\sf{\pi}$ can be taken as $\sf{\frac{22}{7}}$.

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{2\times \dfrac{22}{\cancel{7}}\times 4.2\times \cancel{14}}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{2\times 22\times 4.2\times 2}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{44\times 4.2\times 2}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{44\times 8.4}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\frak{\red{\underline{\underline{369.6\:{cm}^{2}}}}}}$

$\red\bigstar$ TSA of the cylinder:

Substitute the measure of radius and height in the formula of total surface area of cylinder.

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

As mentioned above, the value of $\sf{\pi}$ can be taken as $\sf{\frac{22}{7}}$.

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{2\times \dfrac{22}{7}\times 4.2\times (14+4.2)}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{2\times \dfrac{22}{\cancel{7}}\times \cancel{4.2}\times 18.2}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{2\times 22\times 0.6\times 18.2}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{44\times 0.6\times 18.2}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\sf{44\times 10.92}}$

$\:\:\:\:\:\:\:\:\:\:\implies{\frak{\red{\underline{\underline{480.48\:{cm}^{2}}}}}}$

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Answer 2

Correct Question-:

• Find the Curved Surface Area and Total Surface Area of a Cylinder . Radius = 4.2 cm and Height = 14 cm .

AnswEr-:

• $\underline{\boxed{\star{\sf{\purple{ Curved\:Surface\:Area\:_{(Cylinder)}  \: = \: 369.6cm^{2} }}}}}$
• $\underline{\boxed{\star{\sf{\purple{ Total\:Surface\:Area\:_{(Cylinder)}  \: = \: 480.48cm^{2} }}}}}$

EXPLANATION-:

$\frak{Given \:\: -:} \begin{cases} \sf{The\:Radius \:of\:Cylinder \:\:is\:= \frak{4.2cm}} & \\\\ \sf{The\:Height \:of\:Cylinder \:is \:=\:\frak{14cm}}\end{cases}$

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

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

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

$\frak{Here\:\: -:} \begin{cases} \sf{The\:Radius \:of\:Cylinder \:\:is\:= \frak{4.2cm}} & \\\\ \sf{The\:Height \:of\:Cylinder \:is \:=\:\frak{14cm}} & \\\\ \sf{\pi = \frac{22}{7}} \end{cases}$

Now ,

• $\implies{\sf{\large{Curved\: Surface\:Area _ {Cylinder} = 2 × \frac {22}{7} × 4.2 × 14}}}$
• $\implies{\sf{\large{Curved\: Surface\:Area _ {Cylinder} = 2 × 22 × 4.2 × 2 }}}$
• $\implies{\sf{\large{Curved\: Surface\:Area _ {Cylinder} = 44 × 4.2 × 2 }}}$
• $\implies{\sf{\large{Curved\: Surface\:Area _ {Cylinder} = 44 × 8.4 }}}$
• $\implies{\sf{\large{Curved\: Surface\:Area _ {Cylinder} = 369.6 cm^{2} }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\purple{ Curved\:Surface\:Area\:_{(Cylinder)}  \: = \: 369.6cm^{2} }}}}}$

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

• $\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:_{(Cylinder)}  \: = \: 2 × \pi × Radius ( Height+ Radius) }}}}}$
• $\frak{Here\:\: -:} \begin{cases} \sf{The\:Radius \:of\:Cylinder \:\:is\:= \frak{4.2cm}} & \\\\ \sf{The\:Height \:of\:Cylinder \:is \:=\:\frak{14cm}} & \\\\ \sf{\pi = \frac{22}{7}} \end{cases}$

Now ,

• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × \frac {22}{7} × 4.2 ×( 14+4.2)}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × 22×0.6( 14+4.2)}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 2 × 22 × 0.6 ×18.2}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 44 × 0.6 ×18.2}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 44× 10.92}}}$
• $\implies{\sf{\large{Total\: Surface\:Area _ {Cylinder} = 480.48cm^{2}}}}$

Therefore,

$\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:_{(Cylinder)}  \: = \: 480.48cm^{2} }}}}}$

Hence ,

• $\underline{\boxed{\star{\sf{\purple{ Curved\:Surface\:Area\:_{(Cylinder)}  \: = \: 369.6cm^{2} }}}}}$
• $\underline{\boxed{\star{\sf{\purple{ Total\:Surface\:Area\:_{(Cylinder)}  \: = \: 480.48cm^{2} }}}}}$

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