Problem

16. GEOGRAPHY Earth's circumference is appruximately 25,000 miles. If you could dig a tunnel to the center of the Farth, how long would the tannel be? Round to the nearest twnth mile.

Answer

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Answer

Final Answer: The length of the tunnel would be approximately \(\boxed{3978.87}\) miles.

Steps

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.

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