  Water drains from the conical tank at the rate of 5ftmin14.410Exit rate: 5 ft/mina. What is the relationship between the variables h and r in the figure above?b. How fast is the level of water dropping when h 6 ft?

Question help_outlineImage TranscriptioncloseWater drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the relationship between the variables h and r in the figure above? b. How fast is the level of water dropping when h 6 ft? fullscreen
Step 1

By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r and h remain same at any instant. so, we can get the relationship between r and h. help_outlineImage Transcriptioncloseh10 5 r 4 2 5 h = 2 2 r =h 5 fullscreen
Step 2

Now, we use the formula for volume of cone . By differentiating both sides with respect to t and then by substituting t... help_outlineImage Transcriptionclose1 V Trh=- j 3 1 4 3 75 dh dV dh 4 4 3h dt 75 dt dt 25 dh -5=(6) 25 dt dh 125 - ft /min 144 dt fullscreen

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