Here, we are given that the ratio of the two spheres of ratio 1:8
Let us take,
The radius of 1st sphere = r1
The radius of 1st sphere = r2
So,
Volume of 1st sphere (V1) = `4/3 pi r_1^3`
Volume of 2nd sphere (V2) = `4/3 pi r_2^3`
Now, `V_1/V_2 = 1/8`
`((4/3 pi r_1^3))/((4/3 pi r_2^1)) = 1/8`
`r_1^3/r_2^3 = 1/8`
`r_1/r_2 = 3sqrt(1/8)`
`r_1/r_2 = 1/2` .............(1)
Now, let us find the surface areas of the two spheres
Surface area of 1st sphere (S1) = `4 pi r_1^2`
Surface area of 2nd sphere (S2) = `4 pi r_2^2`
So, Ratio of the surface areas,
`S_1/S_2 = (4pir_1^2)/(4 pi r_2^2)`
`=r_1^2/r_2^2`
` = (r_1/r_2)^2`
Using (1), we get,
`S_1 /S_2 = ( r_1/r_2)^2`
`= (1/2)^2`
`=(1/4)`
Therefore, the ratio of the spheres is 1 : 4 .