Ask Question
12 January, 08:52

A conical (cone shaped) water tower has a height of 12 ft and a radius of 3 ft. Water is pumped into the tank at a rate of 4 ft^3/min. How fast is the water level rising when the water level is 6 ft?

+5
Answers (1)
  1. 12 January, 10:18
    0
    The water rises at a rate of 16 / (9π) ft/min or approximately 0.566 ft/min.

    Step-by-step explanation:

    Volume of a cone is:

    V = ⅓ π r² h

    Using similar triangles, we can relate the radius and height of the water to the radius and height of the tank.

    r / h = R / H

    r / h = 3 / 12

    r = ¼ h

    Substitute:

    V = ⅓ π (¼ h) ² h

    V = ¹/₄₈ π h³

    Take derivative with respect to time:

    dV/dt = ¹/₁₆ π h² dh/dt

    Plug in values:

    4 = ¹/₁₆ π (6) ² dh/dt

    dh/dt = 16 / (9π)

    dh/dt ≈ 0.566

    The water rises at a rate of 16 / (9π) ft/min or approximately 0.566 ft/min.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A conical (cone shaped) water tower has a height of 12 ft and a radius of 3 ft. Water is pumped into the tank at a rate of 4 ft^3/min. How ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers