Some fairly easy trigonometry can answer that question. The vertex angle of an isoceles triangle is given by 2 * arctan(b / (2*h)). "h" in this case is about 250,000 miles (distance from the earth to the moon), and b is about 8,000 miles (diameter of the earth).
Plug the numbers into the formula and you see that, looking at the earth from the moon, the earth would have an apparent diameter of 18.2 degrees, which probably isn't very close to "most of the sky".
My calculations indicate you are off by a factor of 10, or 1 decimal point.
The apparent diameter would be 1.83 degrees.