You and your team come to a slow flowing river that you need to cross. The nearest bridge is 20 miles to the north, too dangerous and too far to trek with your group. You explore the area down river and discover an abandoned shed with a stash of 55-gallon drums (all empty and weighing 35.0 lb each) and a stack of 10-foot planks: You will build a raft. The six members of your team have a combined weight of 925 pounds (assuming everyone was truthful). You also have a four-wheeler (all-terrain vehicle), which weighs 450 lb, and other gear, which adds another 315 lb. Your simple raft design is as follows: a platform of planks with barrels strapped to the bottom. You estimate that the planks weigh about 45.0 lb each, and you will need 20 of them to make a platform that can accommodate everything for the one-way trip. You measure the dimensions of the cylindrical drums and find they have diameter D = 22.5 inches and height h = 33.5 inches (note: not exactly “55 gallons”).

(a) What is the minimum number of barrels that you will need so that the raft will float when fully loaded?

(b) What is the minimum number of barrels you will need if you want the platform to be at least 6 inches above the water when fully loaded?