The radius of the earth is `6.37 xx 10^(6) m` and its mass is `5.975 xx 10^(24) kg`. Find the earth's average density to approopriate significant figures.

Answer

`5.52xx10^(3) kg m^(-3)`

Explanation

Given
Mass of the earth `(M)` Radius of the earth `( R )`
Volume of the earth `(V)`
`= (4)/(3) xx pi R^(3) m^(3) = (4)/(3) xx (3.142) xx ( 6.37 xx 10^(6))^(3)`
Average density `(D)`
` = (Mass)/( Volume) = (M)/(V) = ( 5.975 xx 10^(24))/((4)/(3) xx ( 3.142) xx ( 6.37 xx 10^(6))^(3))`
` = 0.005517 xx 10^(6) kg m^(-3)`
`= 5.52 xx 10^(3) kg m^(-3) ` ( to three significant figures)
The density is accurate only up to three significant figures which is the accuracy of the least accurate factor , namely , the radius of the earth .