To calculate the ratio of the volumes of Saturn and Earth, you can use the formula for the volume of a sphere, which is given by:
Volume = (4/3) * π * (radius^3)
Let's denote the radius of the Earth as "R" and the radius of Saturn as "9R" (given that the radius of Saturn is 9 times that of the Earth).
1. Volume of Earth (VE):
VE = (4/3) * π * R^3
2. Volume of Saturn (VS):
VS = (4/3) * π * (9R)^3
VS = (4/3) * π * 729R^3
Now, let's calculate the ratio of the volumes (VS/VE):
VS/VE = [(4/3) * π * 729R^3] / [(4/3) * π * R^3]
Notice that the (4/3) and π terms cancel out, simplifying the equation:
VS/VE = (729R^3) / (R^3)
VS/VE = 729
So, the ratio of the volumes of Saturn to Earth is 729.
To find out how many Earths can fit inside Saturn, you can take the cube root of this ratio:
Number of Earths that can fit inside Saturn = ∛(VS/VE) = ∛729 = 9
Saturn can accommodate 9 Earths inside it.