Question

The volume of a sphere is directly proportional to the cube of its radius. If the volume of
two spheres are in the ratio 8:1, then what is the ratio of radii of the spheres?​

Answer 1

Given: Volume of sphere 1 = V₁

          Volume of sphere 2 = V₂

Ration of Volume of spheres= V₁/V₂  = 8:1

To find: r₁/r₂ r₁ and r₂ = radii of sphere 1 and 2 respectively

Solution:

Formula used:

Volume of sphere = 4/3 πr³

As, V₁/V₂ = 8/1

     4/3 πr₁³ / 4/3πr₂³ = 8/1

           r₁³ / r₂³ = 8/1

            r₁ / r₂ = $\sqrt[3]{8/1}$

             r₁ / r₂ = 2/1

              r₁ / r₂ = 2:1

Hence, ratio of radii of the spheres = 2:1