Final answer:
The density of the spherical asteroid with a given radius and gravitational acceleration can be calculated using the mass and volume formulas.
Step-by-step explanation:
The density of the spherical asteroid can be found by using the formula: density = mass / volume. However, we need to find the mass of the asteroid first. The mass can be calculated using the formula: mass = (gravitational acceleration * radius^2) / (2GM), where G is the gravitational constant.
Given that the radius of the asteroid is 12.5 km and the gravitational acceleration is 1.33x10^-2 m/s^2, we can substitute these values into the formula to find the mass of the asteroid.
Once we have the mass, we can divide it by the volume of the asteroid (4/3 * π * radius^3) to find the density.
Substituting the values into the formulas, we find that the density of the asteroid is approximately 3.22 g/cm³.