Answer:
They would find [tex]3.14\times 10^{10}[/tex]galaxies.
Explanation:
Given that,
The number of density of galaxies in the universe is 3×10⁻⁶⁸ galaxies /m³.
Assuming that, the astronomers are observing at the center of sphere.
So, they can observe the sphere of space whose radius 10¹⁰ light years.
1 light year = 10¹⁶ meters
10¹⁰ light years =10¹⁰ .10¹⁶ meters
=10²⁶meters
The volume of the space is
=[tex]\frac43 \pi r^3[/tex]
[tex]=\frac43 \pi (10^{26})^3[/tex] m³
[tex]=\frac43 \pi 10^{78}[/tex] m³.
The number of galaxies
= Volume of the space × density
[tex]=(3\times 10^{-68}\ galaxies /m^3)\times(\frac43 \pi . 10^{78}\ m^3)[/tex]
[tex]=10^{10}\pi[/tex] galaxies
= [tex]3.14\times 10^{10}[/tex]galaxies
They would find [tex]3.14\times 10^{10}[/tex]galaxies.
