1. If a snowball melts so that its surface area decreases at a rate of 3 cm 2 /m

Question

1. If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm. (Give your answer correct to 4 decimal places.)

2. Two cars start moving from the same point. One travels south at 56 mi/h and the other travels west at 42 mi/h. At what rate is the distance between the cars increasing one hour later?

3. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 9/10 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall?

Explanation / Answer

1. S= 4 pi r2 = 4 pi (D/2)2 = pi D2

dS/dt= 2 pi D (dD/dt)

3 = 2 pi (9) (d D/dt)

3/(18 pi) = dD/dt

dD/dt=0.0531 cm/min

2. After one hour, one car travels 56 mi and the other travels 4 2 mi .

Let the distance between them is x mi

x2 = 562+ 422

x=70 mi

x2= a2+ b2

x (dx/dt) = a(da/dt) + b(db/dt)   

70(dx/dt) = 56(56)+42(42)

dx/dt=70 mi/h

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