Question

If the ratio of volumes of two spheres is 1 : 8,
then the ratio of their surface areas is
(A) 1:6
(B) 1:4
(C) 1:8
(D) 12​

Answer 1

B option is the correct answer

Answer 2

Option B

Let the volume of the smaller sphere be 4/3πr^3

And that of bigger sphere be 4/3πR^3

Now,

Vol of small sphere/Vol of bigger sphere= 4/3πr^3÷4/3πR^3=1÷8

This gives,

r^3/R^3 =1/8

r/R=1/2

so,

r=1

and R=2

Now the ratio of their surface areas is:-

SA of smaller sphere/SA of bigger sphere=

4π1^2/4π2^2

=1/4

so Option B is correct.