Respuesta :
Answer:
Approximate linear dimension is 2 light years.
Explanation:
Radius of the spiral galaxy r = 62000 LY
Thickness of the galaxy h = 700 LY
Volume of the galaxy = πr²h
= (3.14)(62000)²(700)
= (3.14)(62)²(7)(10)⁸
= 84568×10⁸
= [tex]8.45\times 10^{12}[/tex] (LY)³
Since galaxy contains number of stars = 1078 billion stars ≈ [tex]1.078\times 10^{12}[/tex]
Now volume covered by each star of the galaxy = [tex]\frac{\text{Total volume of the galaxy}}{\text{Number of stars}}[/tex]
= [tex]\frac{8.45\times 10^{12} }{1.078\times 10^{12}}[/tex]
= 7.839 Light Years
Now the linear dimension across the volume
= [tex](\text{Average volume per star})^{\frac{1}{3}}[/tex]
= [tex](7.839)^{\frac{1}{3}}[/tex]
= 1.99 LY
≈ 2 Light Years
Therefore, approximate linear dimension is 2 light years.
