Question

Approximately how many asteroids that are 0.98 km in radius would it take to make a planet which has a radius of 6420.0 km

Answer 1

Answer:

It'd take approximately 6543 asteroids.

Explanation:

In order to calculate the number of asteroids needed to make that planet we first need to determine the volume of each object. To do this we will consider them as spheres and apply the appropriate formula:

$V_{asteroid} = \frac{4*\pi*0.98}{3} = 4.11 \text{ km}^3$

$V_{planet} = \frac{4*\pi*6420}{3} = 26892.03 \text{ km}^3$

The number of asteroids needed are given by the division of planet's volume by the asteroid's volume.

$n = \frac{26892.03}{4.11} = 6543.07$

It'd take approximately 6543 asteroids.