Question

Ratio of volumes of two spheres is 64:27 find the ratio of their radii

Answer 1

volume of 1st sphere / volume of 2nd sphere = 64/27 
⇒ 64/27 = 4/3πR³/4/3πr³
⇒ 64/27 = R³/r³
⇒R/r = ∛64/∛27
⇒R/r = 4/3 
therefore the ration of the sphere's radii = 4:3 
     i hope it helps.............

Answer 2

let the radii of two spheres are R and r

their volumes are V and v
V/v =64/27 (given)

(4/3*πR³)/((4/3*πr³) = 4³/3³
after cancellation
R³/r³=4³/3³

(R/r)³=(4/3)³
therefore
R/r=4/3
R:r =4:3