Question

Topic - Volume and Surface Area
Class - 8
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The total surface area of a solid cylinder is 9372 cm2. If its radius is 21 cm, find its height and volume.
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Best answer will be marked as Brainliest!

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Answer 1

Given :

• Total Surface Area = 9372 cm²
• Radius of Base = 21 cm

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To Find :

• Height of the Cylinder = ?
• Volume of the Cylinder = ?

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Solution :

~ Formula Used :

• Total Surface Area :

${\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\sf{ Total \; Surface \; Area{\small_{(Cylinder)}} = 2 \pi r \bigg\lgroup r + h \bigg\rgroup }}}}}$

• Volume :

${\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\sf{ Volume{\small_{(Cylinder)}} = \pi r²h }}}}}$

Where :

• ➬ ${\sf{ \pi = \dfrac{22}{7} }}$
• ➬ r = Radius
• ➬ h = Height

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~ Calculating the Height :

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ TSA = 2 \pi r \bigg\lgroup r + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 9372 = 2 \times \dfrac{22}{7} \times 21 \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 9372 = 2 \times \dfrac{22}{7} \times 21 \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 9372 = 2 \times \dfrac{22}{\cancel7} \times \cancel{21} \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 9372 = 2 \times 22 \times 3 \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 9372 = 44 \times 3 \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ \dfrac{9372}{44} = 3 \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ \cancel\dfrac{9372}{44} = 3 \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 213 = 3 \bigg\lgroup 21 + h \bigg\rgroup }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ \dfrac{213}{3} = 21 + h }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ \cancel\dfrac{213}{3} = 21 + h }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 71 = 21 + h }}} \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow {\qquad{\sf{ 71 - 21 = h }}} \\ \end{gathered}$

${\qquad \; \; \; {\therefore \; {\underline{\boxed{\orange{\sf{ Height = 50 \; cm }}}}}}}$

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~ Calculating the Volume :

$\begin{gathered} \; \longmapsto {\qquad{\sf{ Volume = \pi r²h }}} \\ \end{gathered}$

$\begin{gathered} \; \longmapsto {\qquad{\sf{ Volume = \dfrac{22}{7} \times {(21)}^{2} \times 50 }}} \\ \end{gathered}$

$\begin{gathered} \; \longmapsto {\qquad{\sf{ Volume = \dfrac{22}{7} \times 21 \times 21 \times 50 }}} \\ \end{gathered}$

$\begin{gathered} \; \longmapsto {\qquad{\sf{ Volume = \dfrac{22}{\cancel7} \times \cancel{21} \times 21 \times 50 }}} \\ \end{gathered}$

$\begin{gathered} \; \longmapsto {\qquad{\sf{ Volume = 22 \times 3 \times 21 \times 50 }}} \\ \end{gathered}$

$\begin{gathered} \; \longmapsto {\qquad{\sf{ Volume = 66 \times 1050 }}} \\ \end{gathered}$

${\qquad \; \; \; {\therefore \; {\underline{\boxed{\purple{\sf{ Volume = 69300 \; {cm}^{3} }}}}}}}$

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~ Therefore :

❛❛ Height of the Cylinder is 50 cm and its Volume is 69300 cm³ . ❜❜

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Answer 2

Given:

• Total Surface Area = 9372 cm²
• Radius of Base = 21 cm

To Find:

• Height of the Cylinder = ??
• Volume of the Cylinder = ??

Formulae Used:

$\\{\bigstar} \; \; {\underline {\boxed {\purple{\bf{ Total \; Surface \; Area= 2 \pi r \bigg( r + h \bigg) }}}}}$

${\bigstar} \; \; {\underline {\boxed {\pink{\bf{Volume{\small_{(Cylinder)}} = \pi r²h}}}}}$

Solution:

★ Finding the height of cylinder by substituting the values in the formula :

$\dashrightarrow {\sf{ TSA = 2 \pi r \bigg( r + h \bigg) }}$

${ \sf{\dashrightarrow {9372 = 2 \times \dfrac{22}{7} \times 21 \bigg( 21 + h \bigg) }} }$

${ \sf{\dashrightarrow {9372 = 2 \times \dfrac{22}{\cancel7} \times \cancel{21} \bigg( 21 + h \bigg)}} }$

${ \sf{\dashrightarrow {9372 = 2 \times 22 \times 3 \bigg(21 + h \bigg) }} }$

${ \sf{\dashrightarrow {9372 = 44 \times 3 \bigg( 21 + h \bigg) }} }$

${ \sf{\dashrightarrow { \cancel\dfrac{9372}{44} = 3 \bigg( 21 + h \bigg)}} }$

${ \sf{\dashrightarrow { 213 = 3 \bigg(21 + h \bigg)}} }$

${ \sf{\dashrightarrow { \cancel\dfrac{213}{3} = 21 + h}} }$

${ \sf{\dashrightarrow { 71 = 21 + h}} }$

${ \sf{\dashrightarrow { 71 - 21 = h}} }$

${ \sf{\dashrightarrow { h = 50 \: cm}} }$

${\bigstar{\red{\underline{\boxed{\sf{Height = 50 \: cm}}}}}}$

Hence, the height of cylinder is 50 cm.

★ Finding the volume of cylinder by substituting the values in the formula :

${ \sf{\dashrightarrow { Volume = \pi r²h}} }$

${ \sf{\dashrightarrow { Volume = \dfrac{22}{7} \times {(21)}^{2} \times 50}} }$

${ \sf{\dashrightarrow { Volume = \dfrac{22}{7} \times 21 \times 21 \times 50}} }$

${ \sf{\dashrightarrow { Volume = 22 \times 3 \times 21 \times 50}} }$

${ \sf{\dashrightarrow { Volume = 66 \times 1050}} }$

${ \sf{\dashrightarrow { 69300 \; {cm}^{3} }} }$

${\bigstar{\red{\underline{\boxed{\sf{volume = 69300 \: cm {}^{2} }}}}}}$

Hence, the volume of cylinder is 69300 cm.