CALCULUS RELATED RATES PROBLEMS AND SOLUTIONS

Problem 1 :

Air is being pumped into a spherical shaped balloon at the rate of 5.4 cubic inches per minute. Find the rate of change of the radius when the diameter is 6 inches.

Solution :

Problem 2 :

The altitude of a triangle is increasing at the rate of 1 cm/min, while the area of the triangle is increasing at the rate of 2 cm²/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm²?

Solution :

Problem 3 :

At noon, ship A and ship B leave from the same point. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships increasing at 4:00 pm?

Solution :

Problem 4 :

PV = C, where P is pressure, V is volume, and C is constant. The pressure is increasing at the rate of 20 kPa/min. Find the rate of change of the volume, when the pressure is 150 kPa and the volume is 600 cm³.

Solution :

Problem 5 :

The string of a kite is perfectly taut and always makes an angle of 30º above horizontal. If the string is let out at a rate of 10 feet per second, how fast is the kite’s height increasing?

Solution :

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