Question

Simple Question!!

If the height of the cylinder is equal to its diameter and the volume is 58212 cm³, then find the CSA and TSA of the cylinder.​

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Answer 1

Hey ❤ here is your answer ⤵️

Given :

Height of the Cylinder = Diameter of the Cylinder

Volume of the Cylinder = 58212 cm³

To Find :

CSA (curved surface area) and TSA (total surface area)

Explanation :

$\longrightarrow$ Let radius of the Cylinder = r cm

. ` . Height of the Cylinder = Diameter of the Cylinder (given)

Hence,

Height of the Cylinder = 2r = Diameter of the Cylinder

Now, we know that

Volume of the Cylinder = πr²h cm³

$\longrightarrow$ and According to the question h = 2r

So,

Volume of the Cylinder = πr²(2r)

Volume of the Cylinder = 2πr³ cm³

$\longrightarrow$ Given volume of Cylinder is 58212 cm³

So,

$\longrightarrow$ Volume of the Cylinder = 2πr³

$\longrightarrow$ 58212 = 2πr³

$\sf \frac{58212}{2} = \frac{22}{7} × r³$

$\sf \frac{29106 × 7}{22} = r³$

1323 × 7 = r³

r³ = 9261

$\longrightarrow$ $\sf r = \sqrt[3]{9261}$

$\longrightarrow$ r = 21 cm

Now, $\sf Radius_{(r)}$ of the Cylinder = 21 cm

then, $\sf Height_{(h)}$ of the Cylinder = ( 2 × 21 ) cm = 42 cm

Now, $\sf CSA_{\green{(Curved \: \: Surface \: \: Area)}_{\red{(Cylinder)}}}$ = 2πrh cm²

$\sf CSA_{\green{(Curved \: \: Surface \: \: Area)}_{\red{(Cylinder)}}} = \bigg( 2 × \frac{22}{7} × 21 × 42 \bigg)$

$\sf CSA_{\green{(Curved \: \: Surface \: \: Area)}_{\red{(Cylinder)}}} = \bigg( 2 × \frac{22}{\cancel{7}} × \cancel{21}^{\: \: \cancel7×3} × 42 \bigg)$

$\sf CSA_{\green{(Curved \: \: Surface \: \: Area)}_{\red{(Cylinder)}}} = \underline{\purple{ 5544 \: \: cm²}}$

Now,

$\sf TSA_{\green{(Total \: \: Surface \: \: Area)}_{\red{(Cylinder)}}}$ = Base Area + CSA

$\sf TSA_{\green{(Total \: \: Surface \: \: Area)}_{\red{(Cylinder)}}}$ = 2πr² + 2πrh

$\sf TSA_{\green{(Total \: \: Surface \: \: Area)}_{\red{(Cylinder)}}}$ = 2πr(r + h)

$\sf TSA_{\green{(Total \: \: Surface \: \: Area)}_{\red{(Cylinder)}}} = 2 × \frac{22}{\cancel7} × \cancel{21}^{\: \: \cancel7 × 3 } (21 + 42)$

$\sf TSA_{\green{(Total \: \: Surface \: \: Area)}_{\red{(Cylinder)}}}$ = 2 × 22 × 3 (63)

$\sf TSA_{\green{(Total \: \: Surface \: \: Area)}_{\red{(Cylinder)}}}$ = 132 (63)

$\sf TSA_{\green{(Total \: \: Surface \: \: Area)}_{\red{(Cylinder)}}} = \underline{\purple{ 8316 \: \: cm²}}$

I hope it helps you ❤️✔️

Answer 2

Given :

• Height of the cylinder is equal to its diameter and the volume is 58212 cm³.

To Find :

• C.S.A and T.S.A of Cylinder .

Solution :

$\longmapsto\tt{Height(h)=Diameter(r)}$

As we know that Diameter is double of Radius . So ,

$\longmapsto\tt{h=2r}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{\pi{{r}^{2}\times{2r}}}$

$\longmapsto\tt{2\pi{{r}^{3}}}$

$\longmapsto\tt{58212=2\times\dfrac{22}{7}\times{{r}^{3}}}$

$\longmapsto\tt{58212\times{7}=44\:{r}^{3}}$

$\longmapsto\tt{\cancel\dfrac{407484}{44}={r}^{3}}$

$\longmapsto\tt{9261={r}^{3}}$

$\longmapsto\tt\bf{21\:cm=r}$

For C.S.A :

$\longmapsto\tt{Height=2r=42\:cm}$

Using Formula :

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

Putting Values :

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

$\longmapsto\tt{44\times{6}\times{21}}$

$\longmapsto\tt\bf{5544\:{cm}^{2}}$

For T.S.A :

Using Formula :

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

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{7}\times{21}\times{(21+42)}}$

$\longmapsto\tt{2\times\dfrac{22}{{\cancel{7}}}\times{21}\times{{\cancel{63}}}}$

$\longmapsto\tt{44\times{21}\times{9}}$

$\longmapsto\tt\bf{8316\:{cm}^{2}}$