Question

volume of a sphere = ³, where r is the radius. The radius of a spherical planet is 6052 km, and its mass is 4.87 × 1027g. Calculate the density of the planet in kilograms per cubic metre (kg/m³). Give your answer in standard form to 3 s.f.​

Answer 1

5240 kg/m³

Explanation:

You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.

Unit conversion

The mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.

The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)

Density

The units of density tell you it is computed by dividing the mass by the volume:

ρ = mass/volume

The volume of the sphere is found using the given formula, so the density is ...

ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)

ρ ≈ 5240 kg/m³

The average density of the planet is about 5240 kg/m³.

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Additional comment

This is comparable to the average density of Earth, which is about 5520 kg/m³.