Question

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

Answer 1

The CSA of the cylinder is 5544 cmsquare and TSA is 8316 CMsqure.

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 :

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

Using Formula :

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

Putting Values :

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

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

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

For T.S.A :

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Using Formula :

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

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Putting Values:

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

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

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

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