Question

the ratio of radii of two cylinders of equal height is 1:3. find the ratio of Their volumes

Answer 1

Let r1 and r2 be radii of two cyclinder and V1, V2  be their volume . 

Let h be height of the two cyclinders, then  

 V1 = πr2h and V2  =  πr22h 

∴  V1 /  V2 =  πr12h /  πr22h  = r12 / r22 = 16 / 25 . 

Answer 2

Hi there !!

Let the common factor be x

So,
Radius of 1st cylinder (r1) = x
Radius of 2nd cylinder (r2)= 3x

Since the heights of both the cylinders are equal,
let
h1 = h
h2 = h

Volume of 1st cylinder :
r1 = x
Height = h

$volume \: = \pi {x}^{2} h$

Volume of 2nd cylinder
r2 = 3x
Height = h

$volume \: = \pi {(3x)}^{2}h$

$volume \: = \pi {9x}^{2} h$

Finding the ratio by writing them as fraction ,
we have,

$\frac{\pi {x}^{2}h }{\pi {9x}^{2}h }$
Cancelling π , x² and h,
we have,

$\frac{1}{9}$

Thus,
the ratio of their volumes is 1 : 9