Solve for each of the following completely:
1. A water tank is in the form of an inverted right circular cone of height 12 m. and the radius of its circular opening is 6 m. If water enters the tank at a rate of 8 m3/hr, how fast is the water level rising when the water is 4m deep?
2. A spherical balloon is being made so that its volume is increasing at the rate of 8 ft3/min. Find the rate at which the radius is increasing when the balloon is 4 ft. in diameter.
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