Find the best solutions to your problems with the help of IDNLearn.com's experts. Our platform provides accurate, detailed responses to help you navigate any topic with ease.

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 :

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

#SPJ4

View image Id1001265
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.