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Name ______________________________________________________ Period _____Date ___________________________Related Rates Problems 1Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 meter per second, how fast is the area of the spill increasing when the radius is 30 meters?Assume that oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 2 feet per second. How fast is the area of the spill increasing when the radius of the spill is 60 feet?A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.How fast is the top of the ladder moving down the wall when its base is 7 feet, 15 feet, and 24 feet from the wall?Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall.A ladder 10 feet long is resting against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 1 foot per second, how fast is the top of the ladder moving down when the bottom of the ladder is 8 feet from the wall?A ladder 10 meters long is leaning against the wall of a building, and the base of the ladder is sliding away from the building at a rate of 3 meters per second. How fast is the top of the ladder sliding down the wall when the base of the ladder is 6 meters from the wall?A ladder 15 feet tall leans against a vertical wall of a home. If the bottom of the ladder is pulled away horizontally from the house at 4 feet per second, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 9 feet from the wall?Each side of a square is increasing at a rate of 6 centimeters per second. At what rate is the area of the square increasing when the area of the square 16 centimeters squared?417195038100A pebble is dropped into a calm pond, causing ripples in the form of concentric circles, on the right. The radius r of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area A of the disturbed water changing?The height of a triangle is increasing at a rate of 1 centimeter per minute while the area of the triangle is increasing at a rate of 2 centimeters squared per minute. At what rate is the base of the triangle changing when the height is 10 centimeters and the area is 100 centimeters squared?A cylindrical tank with a radius of 5 meters is being filled with water at a rate of 3 meters cubed per minute. How fast is the height of the water increasing?The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area when:r = 8 centimetersr = 32 centimetersThe radius r of a sphere is increasing at a rate of 3 inches per minute. Find the rates of change of the volume when:r = 9 inchesr = 36 inchesA spherical balloon is inflated with gas at a rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is:30 centimeters60 centimetersAll edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is:2 centimeters10 centimetersAll edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface area changing when each edge is:2 centimeters10 centimeters ................
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