The mass of the planet Saturn is 5.64x10^24 kg and its radius is 6.00x10^7 m. What is its density?

Since density is mass in kg , volume in m3 , and volume of a round/spherical Saturn V = 4/3 X 22/7 X RADIUS r in meter 3 , now substituting mass and volume in density , we get an expression , density of Saturn = 5.64 x 10^24 kg / 4/3 x 22/7 x 6 x 10^7 m = 6.24 kg/m3

Update : Check out what they said in the Physics Forum: https://in.answers.yahoo.com/question/in...

What kind of hideous thing is that to say to a person trying to seek understanding? Who does that to a person wanting so badly to understand how this universe works?!?

Calculate the volume (assuming that Saturn is a perfect sphere):

V = 4/3πr^3

V = 4/3π(6.0x10^7m)^3

V = 9.047786842 x 10^23

Calculate the density:

ρ = m/V

ρ = 5.64 x 10^24 kg / 9.047786842 x 10^23 m^3

ρ = 6.24 kg/m^3

Therefore the volume of Saturn is 6.24 kg/m^3

Hope this helps!

since you didn't specify UNITS on your density, I'm going to calc g / cm³...

using dimensional analysis

.. ........ ...5.64x10^24kg... ..... ..... ...1000g... ... (1m)³

----- ------ ------ ------ ------ ----- --- x ------ --- x ------- ----- = 6.23x10^-3 g/cm³

..(4/3 x 3.1416 x (6.00x10^7m)³)... ...1kg.. ....(100cm)³

which is of course equal to 6.23 g/L and 6.23 kg/m³... the other answers

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now.. that seems a bit low... right? we all know that

.. (1) density of water = 1g/cm³...

and

.. (2) density of air at STP is about .. d = mw x P / (RT) = 1.29 g/L

so that calculated density of Saturn puts it about 1/5 the density of air at STP and we all know Saturn is a gas giant planet with a potential rocky core so those numbers don't really make sense.. right?

let's google a bit to see if we can figure this out..

.. http://en.wikipedia.org/wiki/Saturn

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that states

.. (1) mass Saturn = 5.68x10^26kg.... 26 not 24

.. (2) equatorial radius = 60268 km = 6.03x10^7m

so it looks like we have a typo on the mass.. let's redo those calcs and correct for it

.. ........ ...5.64x10^26kg... ..... ..... ...1000g... ... (1m)³

----- ------ ------ ------ ------ ----- --- x ------ --- x ------- ----- = 0.623 g/cm³

..(4/3 x 3.1416 x (6.00x10^7m)³)... ...1kg.. ....(100cm)³

which is very close to the accepted 0.687 g/cm³...see the wiki link

d= m/v

m = 5.64 x 10^24 kg

V= 1.33 pi R^3=1.33 x 3.14 x (6x10^7)^3=9.02x10^23 m^3

Then d= 6.25 kg/ m^3