How to find Density/ Radius of planetesimals

[Cherrio]

The ice rich planetesimals that formed the cores of the Jovian planets were about 10 times more massive than Earth. Assuming such an ice ball has a density of 2g cm g^-3, what would its radius be? How does this compare to Earth's radius.


I need Help =\

 

[Kurdt]

What have you tried?

 

[Cherrio]

I was thinking of multiplying the Earths mass by 10 then using the fomula m=dv

and use the formula for volume of a sphere to get r? IDK

 

[Kurdt]

Sounds like a good plan.

 

[Cherrio]

okay so that would be m=dv


10 x 5.97 x 10²⁴ Kg which is 5.97x 10²⁵Kg

then convert from Kg to g 1kg= 1000g

5.97x 10²⁵Kg x 1000 g= 5.97x 10²⁸g
volume of a sphere= (4/3) pi r³

5.97x 10²⁸g= (2g cm^-3)((4/3)pir³)

im not to sure how to isolate R

 

[Kurdt]

You just need a bit of algebraic manipulation. It might help if you use the letters instead of numbers right until the end.

 

[Cherrio]

ok so it would be


m=d 4/3 pi r³

then m/ d(4/3)pi =r³ ?

then r = cubed root of that anwser?

 

[Kurdt]

Yes, that looks good.