Solving Gauss's Law Problem: Excess Electrons in Plastic Sphere

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To determine the number of excess electrons needed to create an electric field of 1250 N/C outside a plastic sphere with a diameter of 23.0 cm, the equation E=Q/4*pi*ε*r^2 was used. The calculated charge was found to be 7.353*10^-9 C. Dividing this charge by the elementary charge (1.602*10^-19 C) resulted in approximately 45.9 billion electrons. The initial confusion arose from using the diameter instead of the radius in calculations. Correcting this error clarified the solution process.
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Homework Statement



How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 23.0cm in diameter to produce an electric field of 1250N/C just outside the surface of the sphere?

Homework Equations



E=Q/4*pi*ε*r^2


The Attempt at a Solution



I've attempted to find the charge using that equation and got 7.353*10^-9. Then to find the number of electrons I did 7.353*10^-9/1.602*10^-19 and I get 45904610632 electrons. It keeps saying I am wrong and I can't figure out why. Can anyone please tell me if I am doing something wrong.

Thanks
 
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NEVERMIND. They threw in 23cm as the diameter and not the radius...
 

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