Question

If the height of a cylinder is equal to its diameter and the volume is 58212 cm3. Find the CSA of cylinder.

Answer 1

Hi.

Good question...Keep Progressing...

Here is your answer---

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Let the height of the Cylinder be h cm
Thus, height = Diameter of the cylinder
       height = 2 x r      [ Diameter = 2 x radius]
        height = 2 x r    ------------------------------------- eq(1)

Given---
    Volume of the Cylinder = 58212 cm^3
                  
We know, Volume of the cylinder = pie x r^2 x h 
                                   58212 = (22/7) x r^2 x 2r     [Using eq(1)]
                                     2 r^3 = 58212(7/22)
                                      2 r^3 = 18522
                                          r^3 = 9261
                                 Thus,  r  = ∛9261
                                             r = 21 cm.
Therefore, height = 2 x r
                              = 2 x 21
                              = 42 cm.

Using the Formula,
   Curved Surface Area of the Cylinder = 2 x pie x r x h
                                                                  = 2 x (22/7) x 21 x 42
                                                                  = 5544 cm^3

Thus, Curved Surface Area of the Cylinder is 5544 cm^3.

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Hope it helps.

Have a nice day.

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 :

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

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

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

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