Sphere 1 has surface area A₁ and volume V₁, sphere 2 has surface area A₂ and volume V₂. If the radius of sphere 2 is six times the radius of sphere 1, what is the ratio of the areas? What is the ratio of the volumes?

Let , radius of sphere 1 is r .

So , radius of sphere 2 is 6r .

Surface area of sphere is given by :

So ,

Volume is given by :

Ratio of sphere 2 by sphere 1 is given by :

Therefore ,  the ratio of area and volume is 36 and 216 respectively .

Hence , this is the required solution .