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anonymous

  • 5 years ago

Ms. Davis loves a good cup of coffee. If she puts on a pot of coffee using coneshaped coffee filter of radius 6 cm and depth 10 cm, and the water begins to drip out through the hole at the bottom at a constant rate of 1.5 cm^3 per second, determine how fast the water level is falling when the depth is 8 cm. Help? :/

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  1. myininaya
    • 5 years ago
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    volume=V depth=d r=radius we want to find d' when d=8cm V=1/3 *pi*r^2*d find derivative we have V'=1/3*pi*2rr'*d+1/3*pi*r^2*d' ..

  2. anonymous
    • 5 years ago
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    Can you show me how you find the derivative?

  3. myininaya
    • 5 years ago
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    you use the product rule we have two triangles so there is a way we can write this with just d' or d without r or r'

  4. myininaya
    • 5 years ago
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    we have to triangles inside the cone so we have 6/r=10/d so r=6d/10=3d/5 so r'=3d'/5

  5. myininaya
    • 5 years ago
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    so we have V'=1/3*pi*2*3d/5*3d'/5*d+1/3*pi*9r^2/5*d' so we can find d' plug in the values for V' and d and then solve for d'

  6. anonymous
    • 5 years ago
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    so I just plug in 8 to V' ?

  7. myininaya
    • 5 years ago
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    i gave us the rate of the volume which was _____________

  8. myininaya
    • 5 years ago
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    mean it gave you*

  9. anonymous
    • 5 years ago
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    1.5cm^3

  10. myininaya
    • 5 years ago
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    yes and the volume is decreasing so it would be negative 1.5cm^3/sec

  11. myininaya
    • 5 years ago
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    they wanted us to find d' when d=8cm

  12. myininaya
    • 5 years ago
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    so we have everything we need to solve for d'

  13. anonymous
    • 5 years ago
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    SO what do I do next?

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