Question

. If the ratio between the volumes of two spheres is 8:27 then find ratio between their surface areas.​

Answer 1

Answer:

4:9

Step-by-step explanation:

let volume & radius of one sphere be v & r respectively

and, let volume & radius of other sphere be V & R respectively

we know,   v:V  = 8:27

that is,        v/V = 8/27

                 (4πr³/3)/(4πR³/3) = 8/27

                 r³/R³ = 2³/3³

                 (r/R)³ = (2/3)³

                 r/R = 2/3

                 (r/R)² = (2/3)²

                 r²/R² = 4/9

      4πr²/4πR² = 4/9     [Multiplying the numerator & denominator by 4π]

but, 4πr² = surface area of circle

s/S = 4/9

s:S = 4:9