Question

the total surface area of a cylinder of radius 5 cm is 660 cm square find the height of the cylinder

Answer 1

Given :

• Total Surface Area of Cylinder is 660 cm² .
• Radius is 5 cm .

To Find :

• Height of Cylinder .

Solution :

$\longmapsto\tt{Radius=5\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{660=2\times\dfrac{22}{7}\times{5(5+h)}}$

$\longmapsto\tt{660\times{7}=44\times{5}\times{(5+h)}}$

$\longmapsto\tt{4620=220(5+h)}$

$\longmapsto\tt{4620=1100+220\:h}$

$\longmapsto\tt{4620-1100=220\:h}$

$\longmapsto\tt{3520=220\:h}$

$\longmapsto\tt{\cancel\dfrac{3520}{220}=h}$

$\longmapsto\tt\bf{16\:cm=h}$

So , The Height of Cylinder is 16 cm .

_______________________

• C.S.A of Cylinder = 2πrh
• T.S.A of Cylinder = 2πr(r+h)
• Volume of Cylinder = πr²h

Here :

• r = Radius
• h = Height
• π = 22/7 or 3.14

_______________________

Answer 2

Given:-

• Total surface area of a cylinder is 660 cm² and radius is 5 cm.

⠀

To find:-⠀

• Height of the cylinder.

⠀

Solution:-

Let,

• the height of the cylinder be h.

⠀

☆Formula used:-

${\dag}\:{\underline{\boxed{\sf{\purple{TSA_{(cylinder)} = 2\pi r (h + r)}}}}}$

⠀

$\tt\longmapsto{660 = 2 \times \dfrac{22}{7} \times 5 (5 + h)}$

⠀

$\tt\longmapsto{660 = \dfrac{220}{7} \times 5 + \dfrac{220}{7} h}$

⠀

$\tt\longmapsto{660 - \dfrac{1100}{7} = \dfrac{220}{7} h}$

⠀

$\tt\longmapsto{\dfrac{4620 - 1100}{7} = \dfrac{220}{7} h}$

⠀

$\tt\longmapsto{220h = 3520}$

⠀

$\tt\longmapsto{h = \dfrac{3520}{220}}$

⠀

$\sf\longmapsto{\boxed{\red{h = 16\: cm}}}$

⠀

Hence,

• the height of the cylinder is 16 cm.

⠀

★More to know :-

$\sf{Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

⠀

$\sf{Area\;of\;Square\;=\;(Side)^{2}}$

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$\sf{Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

⠀

$\sf{Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

⠀

$\sf{Area\;of\;Circle\;=\;\pi r^{2}}$

$\sf{Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

⠀

$\sf{Perimeter\;of\; Square\;=\;4\;\times\;(Side)}$

⠀

$\sf{Perimeter\;of\;Circle\;=\;2\pi r}$