I keep getting 1.26x10^-29 but the correct answer is 4x10^35m^3. Can someone explain what I'm doing wrong?
- NCSLv 71 month ago
volume of a sphere = (4π/3)r³
so for a single proton
V = (4π/3)*(1E-15m)³ = 4.2E-45 m³
You've got 10^80 (1E80) of them, so the total volume of all of the protons is 4.2E-45m³ * 1E80 = 4.2E35 m³ ◄
which should be rounded to 4E35 m³ as you've indicated.
I can't fathom how you got to 1.26x10^-29, so it isn't possible to explain what you're doing wrong. You are 64 orders of magnitude off. Hard to figure.
It might be interesting to note a couple of things.
1. A sphere of that volume has radius 4.6E11 m (about twice Mars' average distance from the sun).
2. If the protons are placed "in contact with one another," the actual volume of the sphere would be about 30% larger due to all of the tiny voids between the spheres.
3. Since all of these protons are positively charged, the forces required to create such an arrangement are unimaginable!
- oubaasLv 71 month ago
Volume of 1 proton Vp = 0.52360*8*10^-45 = 4.188*10^-45 m^3
V sphere Vs :
Vs = n prot.* Vp = 10^80*4.188*10^-45 = 4.188*10^(80-45) = 4.2*10^35 m^3