Related Rates

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Section 6.6 Related Rates
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1. When a circular plate of metal is heated in
an oven its radius increases at a rate of 0.01
cm/min. At what rate is the plates area
increasing when the radius is 50 cm?
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2. The length L of a rectangle is decreasing at
the rate of 2 cm/sec and the width W is
increasing at the rate of 2 cm/sec. When L 12
cm and W 5 cm, find the rates of change of (a)
the area
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2. The length L of a rectangle is decreasing at
the rate of 2 cm/sec and the width W is
increasing at the rate of 2 cm/sec. When L 12
cm and W 5 cm, find the rates of change of (b)
the perimeter
The perimeter does not change
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2. The length L of a rectangle is decreasing at
the rate of 2 cm/sec and the width w is
increasing at the rate of 2 cm/sec. When L 12
cm and w 5 cm, find the rates of change of (c)
the lengths of the diagonals of the rectangle?
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3. Sand falls from a conveyor belt onto a
conical pile at the rate of 10 cubic feet per
minute. The radius of the base of the pile is
always equal to ½ of the altitude. How fast is
the altitude of the pile increasing when the pile
is 5 feet high?
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(No Transcript)
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5. A spherical balloon is inflated with gas at
the rate of 100 cubic feet per minute. a.
Assuming that the gas pressure remains constant,
how fast is the radius of the balloon
increasing at the instant when the
radius is three feet? b. How fast is the
surface area increasing?
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6. A point P moves from left to right along the
curve
at a constant horizontal speed of 3 units per
second. How fast does the y-coordinate of P
increase at the moment when P passes through (2,
4)?
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7. The length of the base of a right triangle is
increasing at the rate of 2 inches per minute.
At the same time, the height of the triangle is
decreasing in such a way that the length of the
hypotenuse remains 10 inches. When the length of
the base is 6 inches, how quickly is the height
of the triangle changing?