## Problem of the Day #57: Geological Expedition
*May 15, 2011*

*Posted by Saketh in : potd , trackback*

Arjun wishes to obtain a sample of Guralite, a rare mineral that is found only on the cliffside of the cone-shaped Mount Rieger. He knows that there is a line running from the top of the mountain down to a point on its base along which deposits of Guralite can be accessed from the surface. Arjun wishes to travel to any point on this line.

Unfortunately, he sets up camp at the point on the mountain’s base that is diametrically opposite to the foot of this line. If Mount Rieger is $10$ km tall with a base of radius $4$ km, determine the shortest path Arjun can take along the mountain’s surface to reach a deposit of Guralite. Then, use a calculator or computer to approximate its length to the nearest thousandth of a kilometer.

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