SOLUTION: Good day!
Please help me with my problem solving.
=> Water is flowing into a conical reservoir 20 ft deep and 10 ft deep across the top at the rate of 15 ft³ per minute. Find ho
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Question 1146721: Good day!
Please help me with my problem solving.
=> Water is flowing into a conical reservoir 20 ft deep and 10 ft deep across the top at the rate of 15 ft³ per minute. Find how fast the surface is rising when the water is 8 ft deep.
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!
(1) Formula for the volume of a cone:
(2) Use the given dimensions of the cone to get the volume formula in terms of a single variable. Since the problem asks for the rate of change of the depth (height), we want a volume formula in terms of h.
The cone has a depth of 20 and a diameter of 10, so a radius of 5. So at all times as the cone is filling, the radius is 1/4 of the depth: r = h/4.
(3) Find the derivative with respect to time:
dV/dt is given; solve for dh/dt when h=8:
ANSWER: the depth of the water in the tank is changing at a rate of 15/(4pi) feet per minute when the depth is 8 feet.
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