2. Soybeans, pouring down from a chute at a constant rate of 2 m3/min, form a conical hil. Assuming that the height of the hill is always twice the radius of its base, find the rate at which the height is increasing at the moment the height is 1 m, and also when the height is 4 m. Hint: The volume of a cone of radius r and height h is V = r²h

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Solve problem C

C. RELATED RATES: Solve the problems below. Show your complete solution with illustration.

10. Supposes a circle is expanding in such a way that its radius is growing at a constant rate of 3
inches per minute. How fast is the area of the circle changing at instant that the radius of the
circle is 12 inches?
11. A 10-ft ladder is leaning against a house on flat ground. The house is to the left of the ladder.
The base of the ladder starts to slide away from the house. When the base has slid to 8 ft from
the house, it is moving horizontally at the rate of 2 ft/sec. How fast is the ladder's top sliding
down the wall when the base is 8 ft from the hoUse?
12. Soybeans, pouring down from a chute at a constant rate of 2 m³/min, form a conical hil.
Assuming that the height of the hill is always twice the radius of its base, find the rate at which
the height is increasing at the moment the height is 1 m, and also when the height is 4 m.
Hint: The volume of a cone of radius r and height h is V = ar?h
Transcribed Image Text:10. Supposes a circle is expanding in such a way that its radius is growing at a constant rate of 3 inches per minute. How fast is the area of the circle changing at instant that the radius of the circle is 12 inches? 11. A 10-ft ladder is leaning against a house on flat ground. The house is to the left of the ladder. The base of the ladder starts to slide away from the house. When the base has slid to 8 ft from the house, it is moving horizontally at the rate of 2 ft/sec. How fast is the ladder's top sliding down the wall when the base is 8 ft from the hoUse? 12. Soybeans, pouring down from a chute at a constant rate of 2 m³/min, form a conical hil. Assuming that the height of the hill is always twice the radius of its base, find the rate at which the height is increasing at the moment the height is 1 m, and also when the height is 4 m. Hint: The volume of a cone of radius r and height h is V = ar?h
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