Question

The Diameter of the base of a right circular cylinder is 42cm and its height is 10cm . Find the area of the curved surface and total surface area. ​

Answer 1

Diameter of the base of the cylinder =42 cm 

∴ r = radius of the base of the cylinder =21 cm 

 h = height of the cylinder =10cm  

∴ curved surface area of the cylinder =  2πrh

          = 2×722×10cm²

          = 2×22×3×10cm2=1320cm²

total surface area of the cylinder = 2πr(h+r)

             = 2×722×21×(10+21)cm²

            = 2×22×3×31cm2=4092 cm²

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• The Diameter of the base of a right circular cylinder is 42cm and its height is 10cm . Find the area of the curved surface and total surface area.

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$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

• Diameter of the base of the Cylinder = 42cm
• Height of the base of the Cylinder = 10cm

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Radius of of the Cylinder = ${\boxed{ \bf { \frac{Diameter}{2} }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{\frac{Diameter}{2} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{\frac{42}{2} \: = \: \cancel\frac{42}{2}}}$

Radius of the Cylinder = ${\boxed{ \bf { 21cm }}}$

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$\large\underline{ \underline{ \sf \maltese{ \: To \: Find :- }}}$

• Curved Surface of the Cylinder ?
• Total Surface of the Cylinder ?

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$\large\underline{ \underline{ \sf \maltese{ \: </strong><strong>Solution</strong><strong>:- }}}$

$\underbrace\purple{\boxed{ \bf \green{Curved \: Surface \: area \: of \: Cyclinder }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: C.S.A \: of \: a \: Cylinder \: = \:2\pi \: \times \: Radius \: \times \: Height }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\bf{C.S.A \: of \: a \: Cylinder \: = \:2 \: \times \: \frac{22}{7} \: \times \: 21\: \times \: 10 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.S.A \: of \: a \: Cylinder \: = \:2 \: \times \: \frac{22}{ \cancel7} \: \times \: \cancel{21}\: \times \: 10 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.S.A \: of \: a \: Cylinder \: = \:2 \: \times \: 22 \: \times \: 3\: \times \: 10 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Curved \: Surface \: area \: of \: Cyclinder\: = \: 1320{cm}^{2} }}}$

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$\underbrace\purple{\boxed{ \bf \green{Total \: Surface \: area \: of \: Cyclinder }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: T.S.A \: of \: a \: Cylinder \: = \:2\pi \: \times \: Radius \: \times \:(\: Height \: + \: Radius \: ) }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\bf{T.S.A \: of \: a \: Cylinder \: = \:2 \: \times \: \frac{22}{7} \: \times \: 21\: \times \: (\: 10 \: + \: 21\: ) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{T.S.A \: of \: a \: Cylinder \: = \:2 \: \times \: \frac{22}{7} \: \times \: 21\: \times \:31 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{T.S.A \: of \: a \: Cylinder \: = \:2 \: \times \: \frac{22}{\cancel7} \: \times \: \cancel21\: \times \:31 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{T.S.A \: of \: a \: Cylinder \: = \:2 \: \times \: 22 \: \times \: \: \times \: 3\: \times \:31 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Total \: Surface \: area \: of \: Cyclinder\: = \: 4092{cm}^{2} }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Curved \: Surface \: area \: of \: Cyclinder \: = \underline {\underline{ 1320{cm}^{2} }}}\\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Total \: Surface \: area \: of \: Cyclinder \: = \underline {\underline{4092{cm}^{2} }}}\\\end{gathered}\end{gathered}$

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