Question

surface area of two sphere are in ratio 16:9. find ratio of their volume.​

Answer 1

Answer:

64:27

Step-by-step explanation:

Let, Radius of first sphere is r and second is R.

So, (4pi×r2)/(4pi×R2)=16/9

=r2/R2=16/9

=r/R=4/3

=r3/R3=64/27

=(4/3pi×r3)/(4/3pi×R3)=64/27

So, the ratio of volume of the two spheres is 64:27.

Answer 2

Surface area of sphere = 4πr²

Sphere A = 4 π R²

Sphere B = 4 π r²

A.T.Q,

Ratio = Sphere A / Sphere B

16 / 9 = 4 π R² / 4 π r²

Cancel 4 π

16 / 9 = R² / r²

On comparing...

R² = 16

=> R = √16

=> R = 4 units

r² = 9

=> r = √9

=> r = 3 units

Ratio of Volume = Volume of Sphere A / Volume of Sphere B

=> Ratio = 4/3 π R³ / 4/3 π r³

Cancel 4/3 π

=> Ratio = R³ / r³

=> Ratio = 4³ / 3³

=> Ratio = 64 / 27

Answer: 64 : 27