Science:Math Exam Resources/Courses/MATH100/December 2015/Question 08 (b)
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Question 08 (b) 

A tank of water in the shape of an inverted circular cone of height 16 m and diameter 20 m at the top is being filled with water at a rate of 2 m^{3} per minute.
(b) Find the rate of change of the height of the water in the tank when the height of the water is 10 m. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Find the relation between the radius of the circle at the top of the water and the height of the water. 
Hint 2 

Recall the volume formula for a cone. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let be the radius of the circle at the top of the water and be the height of the water. Then, the ratio between and is using the property of the similar triangles. On the other hand, by the volume formula of cone, the volume of water can be written as Therefore, by differentiating in terms of on both side, we obtain Since the volume changes at the rate of m^3/min, the rate of change of the height of the water at the height 10m is 
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Nobody voted on this yet Hard Easy 