Question

Find the total surface area and curved surface area of a cylinder of radius 21 and height 49cm​

Answer 1

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: Radius \: of \: the \: cylinder = 21cm \\ \\ \sf \: Height \: of \: cylinder = 49cm$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: (i) \: Total \: surface \: area \: of \: cylinder \\ \\ \sf \: (ii) \: Curved \: surface \: area \: of \: cylinder$

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

$\sf \: Total \: surface \: area = 2\pi r(r + h) \\ \\ \sf \: Curved \: surface \: area = 2\pi rh$

$\large{\red{\underline\bold{{Solution:}}}}$

$\sf \: Let \: the \: radius \: of \: the \: cylinder \: be \: r, \\ \sf \: and \: the \: height \: of \: the \: cylinder \: as \: h$

$\large{\green{\bold{\underline{Then:}}}}$

$\sf \: (i) \: Total \: surface \: area = 2\pi r(r + h) \\ \\ \rightarrow \: \sf Total \: surface \: area = 2 \times \frac{22}{7} \times 21(21 + 49) \\ \\ \rightarrow \: \sf Total \: surface \: area = 2 \times \frac{22}{7} \times 21(70) \\ \\ \rightarrow \: \sf \: Total \: surface \: area = \frac{44}{\cancel7} \times \cancel21 \times 70 \\ \\ \rightarrow \: \sf \: Total \: surface \: area = 44 \times 3 \times 70 \\ \\ \rightarrow \: \sf \: Total \: surface \: area = 9240 \: {cm}^{2}$

$\large{\pink{\bold{\underline{Now:}}}}$

$\sf \: (ii) \: Curved \: surface \: area = 2\pi rh \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 2 \times \frac{22}{7} \times 21 \times 49 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 2 \times \frac{22}{\cancel7} \times \cancel21 \times 49 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 44 \times 3 \times 48 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 6468 \: {cm}^{2}$

$\large{\orange{\bold{\underline{Therefore:}}}}$

$\sf \: The \: total \: surface \: area \: of \: cylinder \: is \\ \sf \: 9240 {cm}^{2} \: and \: curved \: surface \: area \: is \: 6468 {cm}^{2}.$

Answer 2

$\sf\large\orange{\underbrace{ Question : }}$

Find the total surface area and curved surface area of a cylinder of radius 21 cm and height 49 cm.

$\sf\large\orange{\underbrace{ Solution : }}$

★ Given that,

$\rm\: \implies \: Radius (r) _{(Cylinder)}=21cm.$

$\rm\: \implies \: Height (h) _{(Cylinder)}=49cm.$

★ To find,

$\rm\blue{\implies Total\:surface\:area\:_{(Cylinder)}}$

$\rm\blue{\implies Curved\:surface\:area\:_{(Cylinder)}}$

★ Now,

$\tt\purple{\implies Total\:Surface\:area\: of\:cylinder\:= 2\pi \: r(r + h)}$

• Substitute the values

$\bf\:\implies 2 \times\frac{22}{7} \times 21 (21 + 49)$

$\bf\:\implies 2 \times 22 \times 3 \times 70$

$\bf\:\implies 9,240$

$\tt\purple{\implies Curved\:Surface\:area\: of\:cylinder\:= 2\pi \:rh }$

• Substitute the values.

$\bf\:\implies 2 \times\frac{22}{7} \times 21\times 49$

$\bf\:\implies 2 \times 22 \times 3\times 49$

$\bf\:\implies 6,468$

★ Total surface area of cylinder = 9,240 cm².

★ Curved surface area of cylinder = 6,468 cm².

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★ Cylinder formulas :

$\sf\: \implies Total \: surface \: area \: of \: cylinder = 2\pi \:r(r + h)$

$\sf\: \implies Curved \: surface \: area \: of \: cylinder = 2\pi rh$

$\sf\: \implies Volume \: of \: cylinder = \pi r^{2} h$

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