Question

the volume of the cylinder is 6358cu cm height is 28 find its is radius and the curved surface arean

Answer 1

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION\: \: \red{ \mid}}}}}}}}$

$\underline{ \underline{ \bold{ \: \: GIVEN \: \: }}} \to \\ \\ \bold{Volume \: \: of \: \: the \: \: cylinder \: \: = 6358 \: \: cu. \: cm} \\ \\ \bold{Height \: \: of \: \: the \: \: cylinder \:, \: h = 28 \: cm} \\ \\ \\ \underline{ \underline{ \bold{ \: \: TO \: \: FIND \: \: }}} \to \\ \\ \bold{1) \: \: Radius \: \: of \: \: the \: \: cylinder \: \: r = ? } \\ \\ \bold{2) \: Curved \: \: surface \: \: area \: \: of\: \:the \: \: cylinder \: = ? }$

$\bold{(1)} \\ \underline{ \bold{ \: \: We \: \: know \: \: that \: \: }} \\ \\ \bold{Volume \: \: of \: \: a \: \: cylinder = \pi \: r {}^{2} h }$

$\underline{ \bold{ \: \: According \: \: To \: \: Question \: \: }} \\ \\ \bold{Volume =6358 } \\ \\ \bold{ \Longrightarrow \: \pi \: r {}^{2} h = 6358} \\ \\ \bold{ \Longrightarrow \: \frac{22}{7} \times r {}^{2} \times 28 = 6358} \\ \\ \bold{ \Longrightarrow \:88 \: r {}^{2} = 6358 } \\ \\ \bold{ \Longrightarrow \: r {}^{2} = \frac{6358}{88} } \\ \\ \bold{ \Longrightarrow \: r {}^{2} = 72.25} \\ \\ \bold{ \Longrightarrow \: r = \sqrt{72.25 \: } } \\ \\ \bold{ \therefore \: \: r = 8.5}$

$\bold{Radius \: \: of \: \: the \: cylinder \: \: ,\: r = 8.5 \: \: cm}$

$\bold{(2)} \\ \underline{ \bold{ \: \: We \: \: know \: \: that \: \: }} \\ \\ \bold{Curved \: \: surface \: \: area \: \: of \: \: a \: \: cylinder = 2\pi rh} \\ \\ \underline{ \bold{ \: \: Using \: \: this \: \: formula \: \: }} \\ \\ \bold{CSA \: \: of \: \: the \: \: cylinder =( 2 \times \frac{22}{7} \times 8.5 \times 28) \: \: sq.cm} \\ \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1496 \: \: sq. \: cm}$

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: ANSWER \: \: \red{ \mid}}}}}}}}$

$\textbf{ \textsf{1. \: Radius \: \: of \: \: the \: \: cylinder \: = \: \red{8.5 \: cm}}} \\ \\ \textbf{ \textsf{2. \: Curved \: \: surface \: \: area \: \: of \: \: the}} \\ \textbf{ \textsf{cylinder \: = \: \red{ 1496 \: sq.cm} }}$

Answer 2

$\huge\mathtt\red{Solution}$

$\begin{lgathered}\underline{ \underline{ \bold{ \: \: GIVEN \: \: }}} \to \\ \\ \bold{Volume \: \: of \: \: the \: \: cylinder \: \: = 6358 \: \: cu. \: cm} \\ \\ \bold{Height \: \: of \: \: the \: \: cylinder \:, \: h = 28 \: cm} \\ \\ \\ \underline{ \underline{ \bold{ \: \: TO \: \: FIND \: \: }}} \to \\ \\ \bold{1) \: \: Radius \: \: of \: \: the \: \: cylinder \: \: r = ? } \\ \\ \bold{2) \: Curved \: \: surface \: \: area \: \: of\: \:the \: \: cylinder \: = ? }\end{lgathered}$

$\begin{lgathered}\bold{(1)} \\ \underline{ \bold{ \: \: We \: \: know \: \: that \: \: }} \\ \\ \bold{Volume \: \: of \: \: a \: \: cylinder = \pi \: r {}^{2} h }\end{lgathered}$

$\begin{lgathered}\underline{ \bold{ \: \: According \: \: To \: \: Question \: \: }} \\ \\ \bold{Volume =6358 } \\ \\ \bold{ \Longrightarrow \: \pi \: r {}^{2} h = 6358} \\ \\ \bold{ \Longrightarrow \: \frac{22}{7} \times r {}^{2} \times 28 = 6358} \\ \\ \bold{ \Longrightarrow \:88 \: r {}^{2} = 6358 } \\ \\ \bold{ \Longrightarrow \: r {}^{2} = \frac{6358}{88} } \\ \\ \bold{ \Longrightarrow \: r {}^{2} = 72.25} \\ \\ \bold{ \Longrightarrow \: r = \sqrt{72.25 \: } } \\ \\ \bold{ \therefore \: \: r = 8.5}\end{lgathered}$

$\bold{Radius \: \: of \: \: the \: cylinder \: \: ,\: r = 8.5 \: \: cm}$

$\begin{lgathered}\bold{(2)} \\ \underline{ \bold{ \: \: We \: \: know \: \: that \: \: }} \\ \\ \bold{Curved \: \: surface \: \: area \: \: of \: \: a \: \: cylinder = 2\pi rh} \\ \\ \underline{ \bold{ \: \: Using \: \: this \: \: formula \: \: }} \\ \\ \bold{CSA \: \: of \: \: the \: \: cylinder =( 2 \times \frac{22}{7} \times 8.5 \times 28) \: \: sq.cm} \\ \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1496 \: \: sq. \: cm}\end{lgathered}$

$\huge\mathtt\red{Answer}$

$\begin{lgathered}\textbf{ \textsf{1. \: Radius \: \: of \: \: the \: \: cylinder \: = \: \red{8.5 \: cm}}} \\ \\ \textbf{ \textsf{2. \: Curved \: \: surface \: \: area \: \: of \: \: the}} \\ \textbf{ \textsf{cylinder \: = \: \red{ 1496 \: sq.cm} }}\end{lgathered}$