The planets in our solar system can be modeled using spheres. the diameter of jupiter is 142,984. the volume of saturn is 59.9% the volume of jupiter. what is saturn’s diameter, , in kilometers? round your answer to the nearest thousandth.

120,530 km

Step-by-step explanation:

Vs = Volume of Saturn

Vj = Volume of Jupiter

ds = diameter of Saturn

dj = diameter of Jupiter

Step 1) Vs = 59.9% of Vj

Step 2) Vs = 0.599 * Vj

Now, time to explain why I will do what I will...

Short Lesson: Volumes, areas, and lengths have a special relation. Let's say two figures (figure A and figure B) are similar by a scale factor of k. Then:

Side of figure B = k * Side of figure A

Area of figure B = k² * Area of figure A

Volume of figure B = k³ * Volume of figure A

Back to our example. It's given that the ratio between volumes are 0.599. Therefore, the ratio between the lengths must be ∛0.599. (e.g. if the scale factor of sides are 4, then the scale factor of volumes would be 4³ = 64. Reverse operation tells us if we know the scale of the volumes, we should cube root it to find the sides).

Step 3) ds = * 142,984

Step 4) ds = 0.842963831 * 142,984

Step 5) ds = 120530 km

-8

step-by-step explanation: