Sun's End-of-Life Density: Comparing to Earth's Water & Atm.

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Near the end of its life, the sun will expand to a radius close to the Earth's orbital distance, significantly increasing its volume. To estimate the sun's volume at that time, the formula for the volume of a sphere (4/3 π r^3) can be applied using the new radius. This calculation reveals that the average matter density of the sun will decrease, allowing for a comparison with water's density of 1g/cm^3 and Earth's atmospheric density of approximately 10^-3g/cm^3. The distance from the sun to the Earth is about 93 million miles (150 million kilometers). Understanding these comparisons highlights the dramatic changes in the sun's characteristics as it nears its end.
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Near the end of its life, the sun's radius will extend nearly to the distance of the Earth's orbit. I don't understand how to estimate the volume of the sun at that time using the formula for the volume of a sphere (4 pie r^3/3). Using that result, estimate the average matter density of the sun at that time. How does that density compare with the density of water (1g/cm^3)? How does it compare with the density of Earth's atmosphere at sea level (about 10^-3g/cm^3)?
 
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