Question

12. Find the
a) area of curved surface
b) area of total surface
C) volume of a right circular cylinder whose height is 215 cm and radius of the base is 14 cm
(Use -π
22%7​

Answer 1

$\bf\huge\red{ \underline{ \underline{Given\: :-}}}$

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• Height = 215 cm
• radius = 14 cm
• π = 22/7

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$\bf\huge\red{ \underline{ \underline{Solution\: :-}}}$

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a) Curved surface area of the cylinder = ?

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$\bf\large{ \pink{C.S.A \: of \: cylinder = 2 π rh}}$

$\bf\large{ \implies C.S.A =2 \times \frac{22}{ \cancel7} \times \cancel{14 }\times 215} \\ \\ \\ \bf\large{ \implies C.S.A =2 \times 22 \times 2 \times 215 } \: \: \: \\ \\ \\ \bf\large\purple{ \implies C.S.A =18920 \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So, curved surface area of the cylinder is 18920 cm²

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b) Total surface area of the cylinder = ?

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$\bf\large{ \pink{T.S.A \: of \: cylinder = 2 π r(r + h) }}$

$\implies \bf\large{T.S.A = 2 \times \frac{22}{ \cancel{7}} \times \cancel{14} (14 + 215) } \\ \\ \\ \implies \bf\large{T.S.A =2 \times 22 \times 2 \times 229} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \bf\large\purple{ \implies \: 20152 \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So, total surface area of the cylinder is 20152 cm²

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c) Volume of the cylinder = ?

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$\bf\large{\bf\large{\pink{Volume \: of \: cylinder = π {r}^{2}h }}}$

$\implies \bf\large{v= \frac{22}{ \cancel7} \times \cancel{ 14} \times 14 \times 215} \\ \\ \\ \implies \bf\large{v = 22 \times 2 \times 14 \times 215} \: \: \: \\ \\ \\ \bf\large\purple{ \implies v = 132440 \: {cm}^{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So, volume of the cylinder is 132440 cm³