A particular spiral galaxy can be approximated by a thin disk-like volume 35 Thousand Light Years in radius and 8 Hundred Light Years thick. If this Galaxy contains 790 Billion stars, estimate the average distance between the stars in this galaxy. Hint: calculate the average volume per star in cubic Light Years, and then estimate the approximate linear dimension across such a volume. (Indicate your answer to one decimal place.)

The approximate linear dimension is cube root of the average volume, if that is what is confusing you.

avgvolume=total volume/numberSTars
total volume= PI*r^2*thickness

work it in light years as the distance and volume measures

To estimate the average distance between the stars in the given spiral galaxy, we first need to calculate the average volume per star in cubic light years.

To do this, we divide the total volume of the galaxy by the number of stars it contains.

The volume of a cylinder can be calculated using the formula:
Volume = π * radius^2 * height

Let's calculate the volume of the galaxy:
Volume = π * (35,000 light years)^2 * (800 light years)

Next, we divide this volume by the number of stars:
Average volume per star = Volume / 790 billion stars

Now, with the average volume per star calculated, we can estimate the approximate linear dimension across this volume.

We can assume that the volume occupied by a star is roughly spherical. The approximate diameter of this sphere can be calculated using the formula:
Diameter = (3 * Volume / (4 * π))^(1/3)

After calculating the diameter, we can divide it by 2 to get the radius.

Finally, to find the average distance between the stars, we subtract the radius of the star (represented by the diameter) from the thickness of the galaxy and divide it by the number of stars.

Average distance between stars = (Thickness of galaxy - Diameter) / 790 billion

Let's calculate the result now:

Volume = π * (35,000 light years)^2 * (800 light years)
Average volume per star = Volume / 790 billion stars

Diameter = (3 * Average volume per star / (4 * π))^(1/3)
Radius = Diameter / 2

Average distance between stars = (Thickness of galaxy - Diameter) / 790 billion

Now you can plug in the values and calculate the average distance between the stars in the galaxy.