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the circumference of a sphere is 2 π r, where r is the radius of the sphere. the volume of the sphere is 4 3 π r3 , and 1 metric tonne is 1000 kg. assuming that a planet is a perfect sphere with a circumference of 23500 km and an average density of 2.41 g/ml, what is its approximate mass? answer in units of metric tonnes.

Sagot :

id1001265

The planet has an approximate mass of: 5.2815*10^10 metric tones

To solve this problem the formulas and the procedures that we have to use  are:

  • c = 2 * π * r
  • v= (4 *π * r³) / 3
  • d = m/v

Where:

  • c =  circumference of a sphere
  • π = mathematical constant
  • r = radius
  • v= volume
  • d= density
  • m= mass

Information about the problem:

  • c = 23500 km
  • d = 2.41 g/ml
  • π = 3.1416
  • 1 metric tone = 1000 kg
  • r=?
  • v = ?
  • m =?

Applying the circumference of a sphere formula and clearing the radius we get:

c = 2 * π * r

r = 23500 km / 2 * 3.1416

r = 3740.132 km

Applying the volume of the sphere formula we get:

v= (4 *π * r³) / 3

v= (4 *3.1416 * (3740.132 km)³) / 3

v = 2,1915 *10^11 km³

By converting the volume units from (km³) to (ml) we have:

v = 2,1915 *10^11 km³ * 1*10^5 ml/1 km³

v = 2.1915*10^16 ml

Applying the density formula and clearing the mass we get:

d = m/v

m = d * v

m = 2.41 g/ml * 2.1915*10^16 ml

m = 5.2815*10^16 g

By converting the mass units from (g) to (metric tone) we have:

m = 5.2815*10^16 g * 1 kg/1000 g * 1 metric tone/1000 kg

m = 5.2815*10^10 metric tones

What is density?

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

Learn more about density in: brainly.com/question/1354972

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