A solid metal sphere of radius 9 is melted and transformed into 3 identical spheres. What is the ratio of the surface area of one of these spheres to the surface area of the original sphere?

or approximately 0.481

Step-by-step explanation:

Volume of a sphere: 4/3πr³

Surface area of a sphere: 4πr²

The initial sphere of radius 9 has a volume of

When melted into three identical spheres, each must have a volume of

The radius of the smaller spheres must be:

Surface area of each smaller sphere:

Surface area of initial sphere:

The desired ratio is

Exact:

The ratio is 1 to 2  

Step-by-step explanation:

Volume of the original sphere is ≈ 3,053.63 units³

The surface area of the original sphere is ≈ 1,017.88 units²

Volume of one of the small sphere is ≈ 1,017.88 units³

The radius of one of the small sphere is ≈ 6.24 units

The surface area of one of the small sphere is ≈ 489.3 units²

The ratio of the surface area of one of the small sphere to the surface area of the original sphere is

≈

489.3 / 1017.88 ≈ 1 / 2  

The ratio is 1 to 2

x = 3 ± √(5+y)