Question

The volume of two spheres are in the ratio 64:27. Find the ratio of their surface area.​

Answer 1

Answer:16:9 will be the ratio of their surface area

Step-by-step explanation:

Volume of sphere=4$\frac{\pi}{3}$r³

4$\frac{\pi}{3}$R³:4$\frac{\pi}{3}$r³=64:27

4$\frac{\pi}{3}$ cancels each other

hence, R³:r³=64:27

R:r=∛64:27

R:r=4:3

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Surface area of sphere=4πr²

therefore, ratio of surface area will be,

4πR²:4πr²

=R²:r²

=(R:r)²

=(4:3)²

=16:9

Answer 2

Step-by-step explanation:

Let the radius of a first sphere be r and the second sphere be R.

Volume of two spheres=64:27...... Given

Sinve we know that,

Volume of a sphere= 4/3 πr³

therefore, volume of a first sphere/volume of a second sphere=64/27

4/3πr³/4/3πR³=64/27

therefore, r³/R³=64/27

r/R=4/3

Therefore ,ratio of radius of two spheres is 4:3

Total surface area of a sphere=4πr²

total surface area of first sphere=4πr²

total surface area of second sphere=4πR²

therefore their ratio,

4πr²/4πR²

=r²/R²

=4²/3²

=16/9

Therefore ratio of their total surface area is 16/9