Step 1 :The Earth is approximately a sphere, and the distance from the surface to the center of the sphere is the radius.
Step 2 :The circumference of a sphere is given by the formula \(2\pi r\), where \(r\) is the radius.
Step 3 :We can rearrange this formula to solve for \(r\): \(r = \frac{circumference}{2\pi}\).
Step 4 :We can then substitute the given circumference of 25,000 miles into this formula to find the radius, which is the length of the tunnel.
Step 5 :Substituting the values, we get \(r = \frac{25000}{2\pi}\)
Step 6 :Calculating the above expression, we get \(r = 3978.87\)
Step 7 :Final Answer: The length of the tunnel would be approximately \(\boxed{3978.87}\) miles.