Question

If ratio of volumesome of two spheres is 64:27.Find the ratio of their radii.

Answer 1

Volume of a sphere, V = (4/3) π r³

⇒ V ∞ r³ ⇒ ∛V = r

  ∛V₁/∛V₂ = r₁/r₂               (Let, V₁ =64 and V₂ = 27)

⇒∛(64)/∛(27) = r₁/r₂
                                           
⇒ 4/3 = r₁/r₂

⇒r₁ : r₂ = 4 : 3

Answer 2

we know that, volume of a sphere, V = (4/3) π r³
then (4/3) π r³: (4/3) πR³ = 64 : 27
                  r³ : R³ = 64: 27
                  r : R = ∛64 : ∛27
                  r : R = 4 : 3
therefore, the ratio of their radii = 4 : 3