# Diameter of an asteroid

#### liamwpope

I cannot figure out this astronomy problem.

Suppose the average mass of each of 20000 asteroids in the solar system is 10^17kg.

Assuming a spherical shape and a density of 2830 kg/m^3, estimate the diameter of an asteroid having this average mass.

I need to find diameter in km.

#### Debsta

MHF Helper
Ok, so the fact that there are 20 000 asteroids is irrelevant to the problem.

Since $$\displaystyle density = \frac{mass(kg)}{volume(m^3)}$$ then

$$\displaystyle volume = \frac{mass}{density}$$.

So $$\displaystyle volume =\frac{10^{17}}{2830}$$ cubic metres.

Once you know the volume (of a sphere) you should be able to work out the radius or diameter. Have a go.

#### liamwpope

Ok, so the fact that there are 20 000 asteroids is irrelevant to the problem.

Since $$\displaystyle density = \frac{mass(kg)}{volume(m^3)}$$ then

$$\displaystyle volume = \frac{mass}{density}$$.

So $$\displaystyle volume =\frac{10^{17}}{2830}$$ cubic metres.

Once you know the volume (of a sphere) you should be able to work out the radius or diameter. Have a go.
Thank you. I was able to solve it!

Debsta