Question

volume of cylinder is 69300 cube and its height is 50 cm find the the curved surface area​

Answer 1

Given :

• Volume of Cylinder = 69300cm³.
• Height of Cylinder = 50cm.

To Find :

• Curved Surface Area of Cylinder.

Solution :

Firstly we will find Radius of Cylinder :

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cylinder=\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{69300=\dfrac{22}{7}\times{{r}^{2}}\times{50}}$

$\longmapsto\tt{69300\times{7}=1100{r}^{2}}$

$\longmapsto\tt{485100=1100{r}^{2}}$

$\longmapsto\tt{{r}^{2}=\cancel\dfrac{485100}{1100}}$

$\longmapsto\tt{r=\sqrt{441}}$

$\longmapsto\tt\bold{r=21cm}$

So , The Radius of Cylinder is 21cm..

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$\longmapsto\tt{Radius=21cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}$

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{\cancel{7}}\times{\cancel{21}}\times{50}}$

$\longmapsto\tt{44\times{3}\times{50}}$

$\longmapsto\tt\bold{6600{cm}^{2}}$

Therefore , The C.S.A of Cylinder is 6600cm²..

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow height\:of\:cylinder(h)=50cm$

$\sf\dashrightarrow volume\:of\:cylinder=69300cm^3$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow CURVED\:SURFACE\:AREA\:OF\:CYLINDER.$

TAKING TWO CASES,

$\sf\therefore IN\:CASE\:ONE\:,WE\:WILL\:FIND\:RADIUS\:OF\:A\:CYLINDER$

$\sf\therefore IN\:CASE\:TWO\:,WE\:WILL\:FIND\:CURVED\:SURFACE\:AREA\:OF\:CYLINDER.$

✯FORMULA IN USE,

IN CASE 1,

$\large{\boxed{\bf{ \star\:\: VOLUME\:OF\:CYLINDER= \pi r^2h\:\: \star}}}$

IN CASE 2,

$\large{\boxed{\bf{ \star\:\: CURVED\:SURFACE\:AREA\:OF\:CYLINDER= 2\pi rh \:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\large{\boxed{\bf{CASE:-1 }}}$

$\sf\therefore VOLUME\:OF\:CYLINDER= \pi r^2h$

$\sf\implies \dfrac{22}{7} \times (r)^2 \times(50) =69300$

$\sf\implies r^2= \dfrac{69300 \times 7}{50 \times 22}$

$\sf\implies r^2= \dfrac{\cancel{69300} \times 7}{\cancel{50} \times 22}$

$\sf\implies r^2= \dfrac{\cancel{1386} \times 7}{\cancel{22} }$

$\sf\implies r^2= 63 \times 7$

$\sf\implies r^2= 441$

$\sf\implies r= \sqrt{441}$

$\sf\implies r= 21cm$

$\large{\boxed{\bf{ \star\:\: radius= 21cm\:\: \star}}}$

$\large{\boxed{\bf{CASE:-2 }}}$

$\sf\therefore CURVED\:SURFACE\:AREA\:OF\:CYLINDER= 2\pi rh$

$\sf\implies 2\times \dfrac{22}{\cancel{7}} \times \cancel{(21)} \times 50$

$\sf\implies 2 \times 22\times 3 \times 50$

$\sf\implies 6\times 22\times 50$

$\sf\implies 132 \times 50$

$\sf\implies 6600cm^2$

$\large{\boxed{\bf{ \star\:\: curved\:surface\:area\:of\:cylinder= 6600cm^2 \:\: \star}}}$

$\large\underline\bold{ CURVED \:SURFACE\:AREA\:OF\:CYLINDER\:IS\:6600cm^2}$

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