Question

Long
3. The volume of a right circular cylinder is 44,817 cm and height is 7 cm. Find the lateral surface area and the total surface area



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Answer 1

Answer:

Let R be the radius of the circular faces/cylinder.

Then,

Volume of cylinder = 44,817 cm^3

=> pi(R^2)(h) = 44817

=>R^2 = (44817/7) × (7/22)

= 2037.13 cm^2

Therefore, R (apprx.) = 45

So,

area of the 2 Circular faces = 2× pi (R^2)

= (44817/7)×2

= 12804.85 cm^2

Lateral Surface Area = 2×pi×R(h)

= 2 × (22/7)×45×7

= 1980 cm^2

Therefore,

Total Surface Area = 1980 + 12804.85

= 14785 cm^2

Answer 2

Given :

• Volume of Cylinder is 44,817 cm³ .
• Height of Cylinder is 7 cm .

To Find :

• Lateral Surface Area of Cylinder .
• Total Surface Area of Cylinder .

Solution :

Firstly we will Find Radius of Cylinder :

$\longmapsto\tt{Height=7\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{44817=\dfrac{22}{{\not{7}}}\times{{r}^{2}}\times{{\not{7}}}}$

$\longmapsto\tt{44817=22\:{r}^{2}}$

$\longmapsto\tt{\cancel\dfrac{44817}{22}={r}^{2}}$

$\longmapsto\tt{\sqrt{2037.13}=r}$

$\longmapsto\tt\bf{45.13=r}$

Radius of Cylinder is 45.13 ..

_______________________

For Lateral Surface Area :

$\longmapsto\tt{Height=7\:cm}$

$\longmapsto\tt{Radius=45.13\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{{\not{7}}}\times{45.13}\times{{\not{7}}}}$

$\longmapsto\tt{44\times{45.13}}$

$\longmapsto\tt\bf{1985.72\:(Approx.)}$

_______________________

For Total Surface Area :

$\longmapsto\tt{Height=7\:cm}$

$\longmapsto\tt{Radius=45.13\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{7}\times{45.13}\times{(45.13+7)}}$

$\longmapsto\tt{\cancel\dfrac{1985.72}{7}\times{52.13}}$

$\longmapsto\tt{283.67\times{52.13}}$

$\longmapsto\tt\bf{14787.71\:(Approx.)}$