Question

Find the diameter of the base of a cylinder if the lateral surface area is 434π square centimetres and the height is 31 centimetres.​

Answer 1

Given : Lateral Surface Area of the Cylinder is 434π cm² and its height is 31 cm .

To Find : Find the Diameter of the Base

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SolutioN :

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Lateral \; Surface \; Area = 2 \pi rh }}}}}$

Where :

• $\sf{ \pi = \dfrac{22}{7} }$

• r = Radius
• h = Height

$\maltese$ Calculating the Radius :

$\begin{gathered} \qquad \; :\implies \; \sf { LSA = 2 \pi rh } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; \sf { 434 \pi = 2 \times \pi \times r \times 31 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; \sf { \dfrac{ 434 \times \pi }{ 2 \times \pi \times 31 } = r } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; \sf { \dfrac{ 434 \times \cancel{\pi} }{ 2 \times \cancel{\pi} \times 31 } = r } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; \sf { \dfrac{ 434 }{ 2 \times 31 } = r } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; \sf { \dfrac{ \cancel{434} }{ \cancel2 \times 31 } = r } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; \sf { \dfrac{ 217 }{ 31 } = r } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; \sf { \cancel\dfrac{ 217 }{ 31 } = r } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; :\implies \; {\underline{\boxed{\pink{\pmb{\frak{ Radius = 7 \; cm }}}}}} \; {\green{\bigstar}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Diameter :

$\begin{gathered} \qquad \; \; \longrightarrow \; \; \sf { Diameter = 2 \times Radius } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \; \sf { Diameter = 2 \times 7 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; {\underline{\boxed{\red{\pmb{\frak{ Diameter = 14 \; cm }}}}}} \; {\purple{\bigstar}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Diameter of the Cylinder is 14 cm .

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Answer 2

$\underline\bold \red{Thanks \: for \: your \: question} \\ \\ \bold \blue{Given : \: } \\ \\ = > L.S.A = 434π = 2\pi rh \\where π = \frac{22}{7} = > Height = 31 cm \\ \\ \bold \blue{To \: find :} \\ \\ = > Diameter = 2 × radius \\ \\ \bold \red{Solution :} \\ \\ = = > 434\pi = 2 \times \pi \times r \times 31 \\ \\ = = > 434 \cancel{\pi }= 2 \times \cancel{\pi }\times r \times 31 \\ \\ = = > 434 = 62r \\ \\ = = > r = \frac{434}{62} \\ \\ = = > r = \cancel\frac{434}{62} \\ \\ = = > r = \cancel\frac{217}{31} \\ \\ = = > \bold{ r = 7 \: cm} \\ \\ So \: diameter : \\ \\ \: = > 2 \times 7 \\ = > \bold \pink{14 \: cm}$