Question

if the lateral surface are of cylinder is 94.2 cm2 and height is 5cm then find radius of base
it's volume (π=3.14)

Answer 1

Let the radius be r
CSA given= 94.2 cm^2
height given = 5 cm
94.2= 2×3.14×r×5
94.2=10×3.14r
94.2=31.4r
94.2/31.2=r
3 cm=r....

Now Volume = pie×r^2×h
= 3.14×9×5
=>141.3 cm^2

Answer 2

Answer:

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

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{3\ cm}}\put(9,17.5){\sf{5\ cm}}\end{picture}$

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

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

• ↝ 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.

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

${\large{\underline{\underline{\bf{Learn \: More : -}}}}}$

• ⟶ Volume of cylinder = πr²h
• ⟶ T.S.A of cylinder = 2πrh + 2πr²
• ⟶ Volume of cone = ⅓ πr²h
• ⟶ C.S.A of cone = πrl
• ⟶ T.S.A of cone = πrl + πr²
• ⟶ Volume of cuboid = l × b × h
• ⟶ C.S.A of cuboid = 2(l + b)h
• ⟶ T.S.A of cuboid = 2(lb + bh + lh)
• ⟶ C.S.A of cube = 4a²
• ⟶ T.S.A of cube = 6a²
• ⟶ Volume of cube = a³
• ⟶ Volume of sphere = 4/3πr³
• ⟶ Surface area of sphere = 4πr²
• ⟶ Volume of hemisphere = ⅔ πr³
• ⟶ C.S.A of hemisphere = 2πr²
• ⟶ T.S.A of hemisphere = 3πr²

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

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

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