Solutions
KM#11: Size, Mass and Density of the Earth (Level 3)
Mathematical Content: Geometry (radius and circumference of a circle; volume of a sphere); interior angles; Newton's Law of gravitational attraction; formulas for density and force; solving equations
Part 1
Question 1: What is the radius of the Earth?
C = 2πr
40000 = 2πr
Question 2: What is the volume of the Earth?
Part 2
Question 1: What is the mass of the Earth?
To answer this question, follow these steps:
Substitute the values given above in the equation
.
Solve the equation for ME, the mass of the Earth. Use average radius 6.38 x 106 meters
Mg, which is 
.
Question 2: What is the volume of the Earth?
Use average radius 6.38 x 106 meters
Question 3: What is the density of the Earth?
Use answers from 1 and 2:
