Question

The volume of two spheres are in the ratio 27:8, find the ratio of their curved surface areas.

Answer 1

Answer:

Let the radii of the two Spears are

R and r,

Volumes of two Spears are V ,v

According to the problem given ,

V / v = 27 / 8

( 4/3 πR³ )/ ( 4/3πr³ ) = 27 / 8

After cancellation,

R³ / r³ = 3³ / 2³

(R / r )³ = ( 3 / 2 )³

R / r = 3 / 2 ------( 1 )

Let the ratios of the  

Curved surface area of the  

Spears = ( 4πR² ) / ( 4πr² )

= R² / r²

= ( R / r )²

= ( 3 / 2 )²

= 9 / 4  

Therefore ,

Ratios of the curved surface area

of the Spears = 9 : 4

Answer 2

Answer:

V2 / V1 = 27 / 8 = 4/3 pi R2^3 / (4/3 pi R1^3) = (R2 / R1)^3

Likewise the ratio of their surface areas is (R2 / R1)^2

So (27 / 8)^2/3 = (R2 / R1)^2

And (27 / 8)^2/3 = 2.25