4. Given a right circular cone, you put an upsidedown cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upsidedown cone to have the largest possible volume, what fraction of the volume of the larger cone does it occupy? (Let H and R be the height and radius of the large cone, let h and r be the height and radius of the small cone. Use similar triangles to get an equation relating h and r. The formula for the volume of a cone is V : 3im-2h.) Brain Teaser You're sunbathing on the island shown on the map below. The island is six miles from shore at the closest point, and the nearest store is a convenience store seven miles down the beach. If you can row at 4 miles an hour, and you c an walk at 5 miles an hour, where should you land to get a bag of tortilla chips in the least possible time? (Ignore tides, currents, and sharks. N0 fair renting a helicopter.)