Question

Find the area of the sheet required to make closed cylindrical vessel of height 1m and diameter 70 cm?

Answer 1

${\large{\bf{\underline{\underline{\pink{✯ \: Given \: ✯}}}}}}$

• Height = 1 meter
• Diameter = 70 cm

${\large{\bf{\underline{\underline{\pink{✯ \: To \: find \: ✯}}}}}}$

• Area of sheet required.

${\Large{\bf{\red{ ꧁ \: \: { \underline{ \underline{Solution}}} \: \: ꧂}}}}$

${\bf{\footnotesize{✯Converting \: Meter \: into \: Centimeter : }}}$

${ \implies{\bf{ \scriptsize{ Centimeter = Given \: \: meter \: \: no. × 100}}}}$

${ \implies{\bf{ \scriptsize{ Centimeter =1 × 100}}}}$

${ \implies{\bf{ \scriptsize{ Centimeter = 100 \: cm}}}}$

${\bf{\footnotesize{✯ Radius : }}}$

$\: \: \: \: \: \: \: \: \: \: \: { \implies{\bf{ \scriptsize{ Radius = \frac{ Diameter}{ 2}}}}} \\ { \implies{\bf{ \scriptsize{ Radius = \frac{ 70}{ 2}}}}} \\ { \implies{ \scriptsize{ \boxed{ \bf{ Radius = { 35 \: cm}} }}}}$

So, we have :-

• Height = 100 cm
• Radius = 35 cm

${ \bf{ \orange{✯Required \: sheet \: to \: make \: closed}}} \\{ \bf{ \orange{ cylindrical \: vessel : }}}$

So, total surface area is :-

${ \green{\Large{\underline{\boxed{ \bf{ TSA = 2πr (h+r) }}}}}}$

$\\ {\large{\bf{\implies{2 \times \frac{22}{ \cancel7^{1} } \times \cancel{35}^{5 }(100 + 35)}}}}$

${\large{\bf{\implies{2 \times 22 \times 5(135)}}}}$

${\large{\bf{\implies{2 \times 22 \times 675}}}}$

${\underline{\boxed{\large{\bf{\blue{\implies{29,700 \: cm²}}}}}}}$

Area of the sheet required to make closed cylindrical vessel of height 1m and diameter 70 cm is 29700 cm².

${\bf{\footnotesize{✯ In \: \: meter : }}}$

$\: \: \: \: \: \: \: \: \: \: \: { \implies{\bf{ \scriptsize{ Meter = \frac{ Given \: number \: in \: cm }{ 100}}}}} \\ { \implies{\bf{ \scriptsize{ Meter = \frac{29700}{100} }}}} \\ { \implies{ \scriptsize{ \boxed{ \bf{ Meter = { 297 \: {cm}^{2} }} }}}}$

Final answer :-

So, Area of the sheet required to make closed cylindrical vessel of height 1m and diameter 70 cm is 29700 cm² or 297 cm².