Earth mass and density problem

[hndalama]

Homework Statement

The Earth is about 12.70 km in diameter. The Earth’s average density is about 5.5 grams cubic centimeter. A nucleon (the main constituent of an atomic nucleus) has a mass of about 1.67 x 10⁻²⁷ kilograms. If the Earth’s mass is entirely due to its nucleons, how many nucleons are in the Earth?

Homework Equations

Volume = 4/3pi*r³

The Attempt at a Solution

radius =6350m
volume = 4/3pi*(6350)³ = 1.07 *10¹²
density =5.5g/cm³ =5500kg/m³
Earth's mass = density*volume
=5500kg/m³ * 1.07 *10¹²
=5.899 *10¹⁵ kg

number of nucleons= 5.899 *10¹⁵ kg / 1.67 x 10⁻²⁷
= 3.53 * 10⁴²

This answer is wrong but why is it wrong?

 

[phinds]

The Earth is about 12.70 km in diameter.

Uh ... seriously?

 

[hndalama]

Uh ... seriously?

lol, thank you, I thought something was fishy