Question

9. The volume of a cylinder of height 8 cm is 1232 cm°. Find its curved surface area and the
total surface area.​

Answer 1

Given :

• Volume of Cylinder is 1232 cm³ .
• Height of Cylinder is 8 cm .

To Find :

• Curved Surface Area and Total Surface Area of Cylinder .

Solution :

Firstly we will Find Radius :

Using Formula :

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

Putting Values :

$\longmapsto\tt{1232=\dfrac{22}{7}\times{{r}^{2}}\times{8}}$

$\longmapsto\tt{1232\times{7}=176\:{r}^{2}}$

$\longmapsto\tt{\cancel\dfrac{1232}{176}={r}^{2}}$

$\longmapsto\tt{\sqrt{49}=r}$

$\longmapsto\tt\bf{7\:cm=r}$

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For Curved Surface Area :

Using Formula :

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

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{{\not{7}}}\times{{\not{7}}}\times{8}}$

$\longmapsto\tt{44\times{8}}$

$\longmapsto\tt\bf{352\:{cm}^{2}}$

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For Total Surface Area :

Using Formula :

$\longmapsto\tt\boxed{T.S.A\:of\:Cylinder=2\pi{r(r+h)}}$

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{{\not{7}}}\times{{\not{7}}}\:(7+8)}$

$\longmapsto\tt{44\times{15}}$

$\longmapsto\tt\bf{660\:{cm}^{2}}$

Answer 2

$Given\begin{cases}In\:a\:Cylinder \\ Volume=1232 {cm}^{2} \\ Height=8cm \end {cases}$

To find:-

$Curved\:surface\:area{}_{(CSA)}$

$Total\:Surface\:area {}_{(TSA)}$

Solution:-

Let radius=r

as we know that in a Cylinder

${\boxed{Volume={\pi}r {}^{2}h}}$

• Substitute the values

${:}\longrightarrow$ ${\dfrac {22}{7}}×{r}^{2}×8=1232$

${:}\longrightarrow$ $176{r}^{2}=1232$

${:}\longrightarrow$ ${r}^{2}={\dfrac {1232}{176}}$

${:}\longrightarrow$${r }^{2}=49$

${:}\longrightarrow$$r={\sqrt{49}}$

${:}\longrightarrow$$r=7cm$

CSA:-

As we know that

${\boxed{CSA=2{\pi}rh}}$

• Substitute the values

${:}\longrightarrow$$CSA=2×{\dfrac{22}{7}}×7×8$

${:}\longrightarrow$$CSA=44×8$

$\therefore$${\boxed {CSA=352cm {}^{2}}}$

TSA:-

as we know that

${\boxed{TSA=2 {\pi}r (h+r)}}$

• Substitute the values

${:}\longrightarrow$$TSA=2×{\dfrac{22}{7}}×7 (8+7)$

${:}\longrightarrow$$TSA=2×22×15$

$\therefore$${\boxed{TSA=660cm {}^{2}}}$