Question

.The lateral surface area of a cylinder of height 21 cm is 924 cm2
. Find its radius
of the base and its volume.

Answer 1

Given :

• Lateral surface Area = 924 cm²
• Height of Cylinder = 21 cm

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To Find :

• Radius of the Cylinder = ?
• Volume of Cylinder = ?

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Solution :

✯ Formula Used :

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

• ${\underline{\boxed{\purple{\sf{ Volume \; of \; Cylinder = \pi {r}^{2} h }}}}}$

Where :

• ➟ ${\sf{ \pi = \dfrac{22}{7} }}$

• ➟ r = Radius
• ➟ h = Height

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✯ Calcuting the Radius :

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

$\begin{gathered} :\longmapsto \; \; \sf { 924 = 2 \times \dfrac{22}{7} \times r \times 21 } \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { 924 = 2\times \dfrac{22}{\cancel7} \times r \times \cancel{21} } \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { 924 = 2 \times 22 \times r \times 3} \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { 924 = 44 \times r \times 3} \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { \dfrac{924}{44} = r \times 3} \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { \cancel\dfrac{924}{44} = r \times 3} \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { 21 = r \times 3} \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { \dfrac{21}{3} = r } \\ \end{gathered}$

$\begin{gathered} :\longmapsto \; \; \sf { \cancel\dfrac{21}{3} = r } \\ \end{gathered}$

$\begin{gathered} \; \; {\qquad \; \; {\therefore \; \; {\underline{\boxed{\pmb{\red{\frak { Radius = 7 \; cm }}}}}}}} \\ \end{gathered}$

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✯ Calcuting the Volume :

$\begin{gathered} \dashrightarrow \; \; \sf { Volume = \pi {(r)}^{2} h } \\ \end{gathered}$

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

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

$\begin{gathered} \dashrightarrow \; \; \sf { Volume = \dfrac{22}{\cancel7} \times \cancel7 \times 7 \times 21} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Volume = 22 \times 7 \times 21} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Volume = 22 \times 147} \\ \end{gathered}$

$\begin{gathered} \; \; {\qquad \; \; {\therefore \; \; {\underline{\boxed{\pmb{\green{\frak { Volume = 3234 \; {cm}^{3} }}}}}}}} \\ \end{gathered}$

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✯ Therefore :

❛❛ Radius of the base is 7 cm and its volume is 3234 cm³ . ❜❜

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Answer 2

Answer:

7cm and 3234cm^3

Step-by-step explanation:

Given :

Lateral surface Area = 924 cm²

Height of Cylinder = 21 cm

To Find :

Radius of the Cylinder = ?

Volume of Cylinder = ?

Solution :

✯ Formula Used :

Where :

➟  

➟ r = Radius

➟ h = Height

✯ Calcuting the Radius :

✯ Calcuting the Volume :

✯ Therefore :

❛❛ Radius of the base is 7 cm and its volume is 3234 cm³

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