Question

csa of cylinder is 3980cm*2 and its volume is 41580cm*3 find height and radius​

Answer 1

❏ Question:-

@ C.S.A. of cylinder is 3980cm*2 and its volume is 41580cm*3 find height and radius.

❏ Solution:-

✦Given:-

•C.S.A. of that cylinder is = 3980 cm²

•Volume(v) of that cylinder is = 41580 cm³

✦To Find :-

• height of that cylinder = ?

• radius of that cylinder = ?

✦Explanation :-

let , the height and radius of the cylinder are h and r respectively .

$\sf\longrightarrow C.S.A=2\pi r h$

$\sf\longrightarrow \frac{\cancel{3980}}{\cancel2}=(\pi r h)$

$\sf\longrightarrow\large{ (\pi r h)=1990}$

Now,

$\sf\longrightarrow Volume=\pi r{}^{2}h$

$\sf\longrightarrow 41580=(\pi rh)\times r$

$\sf\longrightarrow 41580=1990\times r$

$\sf\longrightarrow\frac{ \cancel{41580}}{\cancel{1990}}= r$

$\sf\longrightarrow \boxed{\large{ \red{r=20.9 \:cm}}}$ (almost).

$\therefore$ Radius of that cylinder is = 20.9 cm.

Now,

$\sf\longrightarrow\large{ (\pi r h)=1990}$

$\sf\longrightarrow \frac{22}{7}\times 20.9\times h=1990$

$\sf\longrightarrow h=1990\frac{7}{22\times20.9}$

$\sf\longrightarrow \boxed{\red{\large{h=30.3 \:cm}}}$ (almost).

$\therefore$ Height of that cylinder is = 30.3 cm.

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❏ Formula Used:-

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✦ CYLINDER✦

For a right circular cylinder of base radius r and height h,

$\sf\longrightarrow\boxed{ L.S.A=2\pi r h}$

$\sf\longrightarrow\boxed{ T.S.A.=2\pi r (r+h)}$

$\sf\longrightarrow \boxed{Volume=\pi r{}^{2}h}$

Where, •L.S.A.=Curved Surface area.

•T.S.A.=Total Surface Area.

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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Answer 2

Answer:

Height = 30.3 cm and Radius ≅ 20.9 cm

Step-by-step explanation:

We Have :-

CSA Of Cylinder = 3980 cm²

Volume Of Cylinder = 41580 cm³

To Find :-

Height and Radius of Cylinder

Formula Used :-

CSA Of Cylinder = 2πrh

Volume Of Cylinder = πr²h

Solution :-

$3980 = \frac{2*22*r*h}{7} \\\\\frac{3980 *7}{2*22} = rh\\\\rh = 633.20$

$h = \frac{633.20}{r} \\\\41580 = \frac{22*r^{2}*h }{7} \\\\41580 = \frac{22*r^{2} *633.20 }{7r} \\\\\frac{41580*7}{22*633.20} = r\\\\r = 20.90 cm\\\\h = \frac{633.20}{20.9} \\\\h = 30.30 cm$

Height = 30.3 cm and Radius ≅ 20.9 cm