Question

the radius of a cylinder is 7cm if it volume is 2002. Find its height and CSA ​

Answer 1

AnSwer -:

Height of cylinder = 13.005cm

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TSA of cylinder = 879.4198 sq. cm

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Explanation-:

Volume of cylinder-:

“V = πr^2 h”

Here ,

V = Volume

R = Radius

H = height

π = 22/7 or 3.14

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Given ,

Height = ??

Volume = 2002 cm ^3

Radius = 7 cm

π = 3.14


To find

Height= v / πr^2

= 2002 cm^3 / π x 7 x 7

= 2002 cm^3 / π x 49

= 2002 cm^3 / 3.14 x 49

= 2002 cm^2 / 153.86

= 13.005

Height of cylinder = 13.005cm

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Given ,

Height = 13.005

Volume = 2002 cm ^3

Radius = 7 cm

π = 3.14


Formula of TSA of cylinder-:

TSA -: 2πr(h+r)

= 2 x 3.14 x 7 ( 13.005 + 7)

= 6.28 x 7 ( 20.005)

=. 43.96 x 20.005

= 879.4198 sq. cm

TSA of cylinder = 879.4198 sq. cm

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Final Answer-:

Height of cylinder = 13.005cm

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TSA of cylinder = 879.4198 sq. cm

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Answer 2

${ \bold \green { \underline{\large{Required \: Answer : - }}}} \:$

Radius = 7 cm

Volume = 2002 cm³

$\large\tt\underline{\orange{Formula\:of\:volume\:of\:cylinder\::-}}$

$\large\boxed{\sf{\red{πr^2h}}}$

We know that volume of cylinder is 2002 cm³.

$\therefore$ πr²h = 2002 cm³.

Let's put values :-

: $\dfrac{22}{7} × 7 × 7 × h = 2002$

: $\dfrac{22}{\cancel{7}} × \cancel{7} × 7 × h = 2002$

: $22 × 7 × h = 2002$

: $154 × h = 2002$

: $h = \dfrac{2002}{154}$

: $h = \cancel{\dfrac{2002}{154}}$

: $h = 13$

$\therefore$ $\large\boxed{\sf{\pink{Height\: = \:13\:cm}}}$

Now

$CSA \: of \: cylinder \: = 2πrh$

So, let's put the values :-

: $\implies$ $2 × \dfrac{22}{7} × 7 × 13$

: $\implies$ $2 × \dfrac{22}{\cancel{7}} × \cancel{7} × 13$

: $\implies$ $2 × 22 × 13$

: $\implies$ $572 cm^2$

SO,

$\large\boxed{\sf{\purple{Curved\:surface\:area\:(CSA)\: = \:572\: cm^2}}}$

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