Question

Suppose there are 106 (1 million) asteroids that are 0.87 km in radius. If they were all combined into a single sphere, calculate the radius of this sphere in km.

Answer 1

87km

Explanation:

Volume is proportional to radius cubed, so radius is proportional to the cube root of volume.

Increase volume by a factor of 10^6 and radius increases by a factor of the cube root of 10^6, which is 10^(6/3) = 10^2 = 100.

100 * 0.87 km = 87 km