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 .

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.