Question

The volume of a cylinder in cm cube is equal to curved surface of a cyclinder in cm square .Find the diameter of cylinder​ (How the radius is 2)​

Answer 1

$\huge\it\red{\underline{\underline{Answer:}}}$

$\sf{The \ diameter \ of \ cylinder \ is \ 4 \ cm}$

$\huge\it\orange{Given:}$

$\sf{For \ cylinder, }$

$\sf{Volume=Curved \ surface \ area}$

$\huge\it\pink{To \ find:}$

$\sf{The \ diameter \ of \ the \ cylinder. }$

$\huge\it\green{\underline{\underline{Solution:}}}$

$\sf{For \ cylinder, }$

$\sf{Let \ Radius \ be \ r \ cm \ and \ height \ be \ h \ cm}$

$\boxed{\sf{Curved \ surface \ area=2\pi\times \ r\times \ h}}$

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

$\sf{According \ to \ the \ given \ condition}$

$\sf{For \ cylinder, }$

$\sf{Volume=Curved \ surface \ area}$

$\sf{\therefore{\pi\times \ r^{2}\times \ h=2\pi\times \ r\times \ h}}$

$\sf{\therefore{r=2 \ cm}}$

$\sf{But, \ diameter=2\times \ r}$

$\sf{\therefore{Diameter=2\times2}}$

$\sf{\therefore{Diameter=4 \ cm}}$

$\sf\purple{\tt{\therefore{The \ diameter \ of \ cylinder \ is \ 4 \ cm}}}$

Answer 2

Given ,

The volume of a cylinder in cm² is equal to the curved surface of a cyclinder in cm²

We know that , the volume and curved surface area of cylinder is given by

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

Thus ,

π(r)²h = 2πrh

r = 2 cm

Therefore , the radius of cylinder is 2 cm

Since , Diameter = 2 × radius

Thus ,

Diameter = 2 × 2 = 4 cm

Hence , the diameter of cylinder is 4 cm