Question

the surface area of two spheres are in the ratio 1:4 ,then the ratio of their volumes is

Answer 1

let , the radius of first sphere be ' r1' and radius of second sphere be ' r2'

according to question,

area 1 : area 2 = 1 : 4

4πr1^2 : 4πr2^2 = 1: 4

r1 / r2 = √( 1 / 4)

r1 / r2 = 1 / 2 => 1 : 2

then ratio of their volumes will be

4/3 πr1^3 : 4 /3 πr2^3

r1^3 : r2^3 = 1^3 : 2^3

= 1 : 8

therefore , ratio of the volumes of Two sphere are 1 : 8.
_______________________________
Your answer V1 : V2 = 1 : 8
_______________________________