Question

If the ratio of the volume of two spheres is 1 : 8, then the ratio of their surface area is ​

Answer 1

Answer:

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

Answer 2

Let the volume of two spheres be x and 8x

then its volume is given by..

x = (4/3)πr³.....(1)

8x = (4/3)πR³.....(2)

Put the value of equation 1 in 2..

we get..

8[(4/3)πr³] = (4/3)πR³

8 = R³/r³

2 = R/r

R = 2r

Surface area of two spheres is given by..

surface area of small sphere is 4πr²

then large sphere is

4πR² => 4π(2r)² => 16πr²

so,

1:4 is the ratio of surface areas of two spheres.