The density of an object equals its mass divided by its volume. The mass of Earth is 6 * 10²⁴ kg and its radius is 4*10³ miles. The mass of the Sun is 2* 10³³ g and its radius is 7 * 10⁵ km. Determine the ratio of the Earth's density to that of the Sun. A) 4 *10^-1 B) 4 * 10² C) 4 * 10⁰ D) 4 *10¹ E) None of these choices

Question

Quizplus · Accepted Answer

1. Convert the mass of Earth from kg to g.
6.0 x 10^24 kg = 6.0 x 10^27 g

2. Convert the radius of Earth from miles to cm.
4.0 x 10^10 miles = 6.44 x 10^13 cm

3. Calculate the volume of Earth.
V = (4/3)πr^3 = (4/3)π(6.44 x 10^13)^3 = 1.08 x 10^28 cm^3

4. Calculate the density of Earth.
ρ = m/V = (6.0 x 10^27 g) / (1.08 x 10^28 cm^3) = 5.56 g/cm^3

5. Convert the mass of the Sun from g to kg.
2.0 x 10^33 g = 2.0 x 10^30 kg

6. Convert the radius of the Sun from km to cm.
7.0 x 10^5 km = 7.0 x 10^8 cm

7. Calculate the volume of the Sun.
V = (4/3)πr^3 = (4/3)π(7.0 x 10^8)^3 = 1.41 x 10^27 cm^3

8. Calculate the density of the Sun.
ρ = m/V = (2.0 x 10^30 kg) / (1.41 x 10^27 cm^3) = 1.42 g/cm^3

9. Calculate the ratio of the density of Earth to the density of the Sun.
5.56 g/cm^3 / 1.42 g/cm^3 = 3.9

Rounded to one significant figure, the ratio is 4, which corresponds to choice C.

The Density of an Object Equals Its Mass Divided by Its