Question

If the lateral surface area of a cylinder is 94.2 and it's height is 5cm,then find (i) radius of it's base (ii) it's volume.

Answer 1

HII HERE IS YOUR SOLUTION...., : )

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Answer 2

${\large{\underline{\underline{\bf{Given : -}}}}}$

↝ LSA of cylinder = 94.2 cm².

↝ Height of cylinder = 5 cm

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{To \: Find : -}}}}}$

↝ Radius of cylinder

↝ Volume of cylinder

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Using \: Formulae: -}}}}}$

↝ L.S.A of cylinder = 2πrh

↝ Volume of cylinder = πr²h

$\green\bigstar$ Where

↠ L.S.A = Lateral surface area

↠ π = 3.14

↠ r = radius

↠ h = height

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Solution: -}}}}}$

$\green\bigstar$ Here :-

↠ L.S.A = 94.2 cm²

↠ π = 3.14

↠ h = 5 cm

↠ r = ?

$\begin{gathered}\end{gathered}$

$\green\bigstar$ According to the question :-

$\dashrightarrow\sf{L.S.A_{(cylinder)}= 2 \pi rh }$

$\dashrightarrow\sf{94.2 \: {cm}^{2} = 2 \times 3.14\times r \times 5}$

$\dashrightarrow\sf{94.2 \: {cm}^{2} = 10 \times 3.14\times r }$

$\dashrightarrow\sf{94.2 \: {cm}^{2} = 31.4\times r }$

$\dashrightarrow\sf{94.2 \: {cm}^{2} = 31.4r}$

$\dashrightarrow\sf{r = \dfrac{94.2}{31.4}}$

$\dashrightarrow\sf{r = \dfrac{94.2 \times 10}{31.4 \times 10}}$

$\dashrightarrow\sf{r = \dfrac{942}{314}}$

$\dashrightarrow\sf{r = \cancel{\dfrac{942}{314}}}$

$\dashrightarrow\sf{r =3 \: cm}$

$\bigstar\red{\underline{\boxed{\bf{Radius \: of \: cylinder=3 \: cm}}}}$

∴ The Radius of Cylinder is 3 cm.

$\begin{gathered}\end{gathered}$

$\green\bigstar$ Now, Calculating the volume of cylinder :-

$\dashrightarrow\sf{Volume_{(Cylinder)} = \pi {r}^{2} h}$

$\dashrightarrow\sf{Volume_{(Cylinder)} = 3.14 \times {3}^{2} \times 5}$

${\dashrightarrow\sf{Volume_{(Cylinder)} = 3.14 \times 3 \times 3\times 5}}$

${\dashrightarrow\sf{Volume_{(Cylinder)} = 3.14 \times 9\times 5}}$

${\dashrightarrow\sf{Volume_{(Cylinder)} = 3.14 \times 45}}$

${\dashrightarrow\sf{Volume_{(Cylinder)} = 141 \: {cm}^{2} }}$

$\bigstar{\red{\underline{\boxed{\bf{Volume \: of \: cylinder = 141 \: {cm}^{2}}}}}}$

∴ The volume of cylinder is 141.1 cm².

$\begin{gathered}\end{gathered}$

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