Question

a thin cardboard sheet is used to cover the curved surface of a cylinder with radius 10.5cm , height 30cm find the area of cardboard sheet used ​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Curved surface area of cylinder is covered with cardboard sheet

• Radius of cylinder is 10.5 cm

• Height of cylinder is 30 cm

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Area of cardboard sheet used

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Area of cardboard sheet used will be equal to the curved surface area of cylinder as it is given that the sheet is used to cover the curved surface area of cylinder

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$\underline{ \underline{\bold{\texttt{Curved surface area of cylinder :}}}}$

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➠ 2πrh

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Where ,

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• r = Radius of cylinder

• h = Height of cylinder

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$\underline{ \underline{\bold{\texttt{Curved surface area kf given cylinder :}}}}$

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• r = 10.5 cm

• h = 30 cm

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⟮ Putting the above values in ⓵ ⟯

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: ➜ 2πrh

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: ➜ $\sf 2 \times \dfrac { 22 } { 7 } \times 10.5 \times 30$

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: ➜ $\sf \dfrac { 44 \times 105 \times 3 } { 7 }$

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: ➜ $\sf \dfrac { 44 \times 315 } { 7 }$

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: ➜ $\sf \dfrac {13860 } { 7 }$

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: : ➨ $\sf 1980 \: sq. \: cm.$

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• Hence the area of cardboard sheet used is 1980 sq. cm.

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Additional information

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Volume of cylinder

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• πr ²h

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Where ,

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➻ r = Radius of cylinder

➻ h = Height of cylinder

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Total surface area of cylinder

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• 2πr(h + r)

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➻ r = Radius of cylinder

➻ h = Height of cylinder

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• Curved surface area of cylinder is covered with cardboard sheet

• Radius of cylinder is 10.5 cm

• Height of cylinder is 30 cm

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• Area of cardboard sheet used

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

Area of cardboard sheet used will be equal to the curved surface area of cylinder as it is given that the sheet is used to cover the curved surface area of cylinder

$\:\:$

$\underline{ \underline{\bold{\texttt{Curved surface area of cylinder :}}}}$

$\:\:$

➠ 2πrh

$\:\:$

Where ,

$\:\:$

r = Radius of cylinder

h = Height of cylinder

$\:\:$

$\underline{ \underline{\bold{\texttt{Curved surface area kf given cylinder :}}}}$

$\:\:$

r = 10.5 cm

h = 30 cm

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ 2πrh

$\:\:$

: ➜ $\sf 2 \times \dfrac { 22 } { 7 } \times 10.5 \times 30$

$\:\:$

: ➜ $\sf \dfrac { 44 \times 105 \times 3 } { 7 }$

$\:\:$

: ➜ $\sf \dfrac { 44 \times 315 } { 7 }$

$\:\:$

: ➜ $\sf \dfrac {13860 } { 7 }$

$\:\:$

: : ➨ $\sf 1980 \: sq. \: cm.$

$\:\:$

• Hence the area of cardboard sheet used is 1980 sq. cm.

$\:\:$