## 13-14 Water flowing into trapezoidal trough

Problem 13
A trapezoidal trough is 10 ft long, 4 ft wide at the top, 2 ft wide at the bottom and 2 ft deep. If water flows in at 10 ft3/min, find how fast the surface is rising, when the water is 6 in deep.

Problem 14
For the trough in Problem 13, how fast the water surface is rising when the water is 1 foot deep.

## 04-05 Water flowing into triangular trough

Problem 04
A triangular trough 10 ft long is 4 ft across the top, and 4 ft deep. If water flows in at the rate of 3 ft3/min, find how fast the surface is rising when the water is 6 in deep.

Problem 05
A triangular trough is 10 ft long, 6 ft wide across the top, and 3 ft deep. If water flows in at the rate of 12 ft3/min, find how fast the surface is rising when the water is 6 in deep.

## 01-02 Water flowing into cylindrical tank

Problem 01
Water is flowing into a vertical cylindrical tank at the rate of 24 ft3/min. If the radius of the tank is 4 ft, how fast is the surface rising?

Problem 02
Water flows into a vertical cylindrical tank at 12 ft3/min, the surface rises 6 in/min. Find the radius of the tank.

Problem 02
Water flows into a vertical cylindrical tank at 12 ft3/min, the surface rises 6 in/min. Find the radius of the tank.

## Time Rates

Time Rates
If a quantity x is a function of time t, the time rate of change of x is given by dx/dt.

When two or more quantities, all functions of t, are related by an equation, the relation between their rates of change may be obtained by differentiating both sides of the equation with respect to t.