1. Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right circular cone 20 ft deep and 20 ft in diameter at the top. If water level is rising at the rate of 1⁄4 ft/min, how fast will the water be leaking out when the water level is 12 ft deep?
Solve the following using time rates(derivative). Show complete and detailed solution.
1. Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right circular cone 20 ft deep and 20 ft in diameter at the top. If water level is rising at the rate of 1⁄4 ft/min, how fast will the water be leaking out when the water level is 12 ft deep?
2. A cylindrical container with no top is to be constructed for a fixed amount of money. The cost of material for the bottom is 3 dollars per square inch, and the cost of material for the lateral surface is 2 dollars per square inch. Find the relationship between the radius and height of the container having the greatest volume.
3. You are standing on the bank of a river that is 1 mile wide and want to get to a town on the opposite bank, 1 mile upstream. You plan to row on a straight line to some point R on the opposite bank and then walk the remaining distance along the bank. To what point R should you row to reach the town in the shortest possible time, if you can row at 4 miles/hr and walk at 5 miles/ hr?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
