Question

A cylinder has hemispherical ends
having radius 14 cm and height 50
cm. Find the total surfacearea
​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• A cylinder has hemispherical ends

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• Radius is 14 cm

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• Height is 50 cm

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• The total surface area

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

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

$\:\:$

➠ 2πrh

$\:\:$

$\underline{\bold{\texttt{Outer surface area of hemisphere :}}}$

$\:\:$

➠ 2πr²

$\:\:$

$\underline{\bold{\texttt{Total surface area of given object :}}}$

$\:\:$

Curved surface area of cylinder + 2(Outer surface area of hemisphere)

$\:\:$

➜ 2πrh + 2 × 2πr²

$\:\:$

➜ 2πrh + 4πr²

$\:\:$

➜ 2πr(h + 2r) -------- (1)

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• Height = 50 cm

• Radius = 14 cm

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⟮ Putting these values in (1) ⟯

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➜ 2πr(h + 2r)

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➜ $\sf 2 × \dfrac { 22 } { 7 } × 14(50 + 2 × 14)$

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➜ $\sf 2 × \dfrac { 22 } { \cancel 7 } × \cancel { 14} (78)$

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➜ 2 × 22 × 2 × 78

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➜ 88 × 78

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➨ 6864 sq. cm

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• Hence total surface area of given object is 6864 sq. cm.

$\:\:$

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Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• A cylinder has hemispherical ends

$\:\:$

• Radius is 14 cm

$\:\:$

• Height is 50 cm

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• The total surface area

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

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

$\:\:$

➠ 2πrh

$\:\:$

$\underline{\bold{\texttt{Outer surface area of hemisphere :}}}$

$\:\:$

➠ 2πr²

$\:\:$

$\underline{\bold{\texttt{Total surface area of given object :}}}$

$\:\:$

Curved surface area of cylinder + 2(Outer surface area of hemisphere)

$\:\:$

➜ 2πrh + 2 × 2πr²

$\:\:$

➜ 2πrh + 4πr²

$\:\:$

➜ 2πr(h + 2r) -------- (1)

$\:\:$

• Height = 50 cm

• Radius = 14 cm

$\:\:$

⟮ Putting these values in (1) ⟯

$\:\:$

➜ 2πr(h + 2r)

$\:\:$

➜ $\sf 2 × \dfrac { 22 } { 7 } × 14(50 + 2 × 14)$

$\:\:$

➜ $\sf 2 × \dfrac { 22 } { \cancel 7 } × \cancel { 14} (78)$

$\:\:$

➜ 2 × 22 × 2 × 78

$\:\:$

➜ 88 × 78

$\:\:$

➨ 6864 sq. cm

$\:\:$

• Hence total surface area of given object is 6864 sq. cm.

$\:\:$

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