Calculus Help

The County Roads Department is stockpiling salt for use next winter. The salt is being unloaded from
railroad cars by a conveyor belt at a rate of 20 cubic feet per minute. The salt falls into a conical pile
whose diameter at the base is four times the height of the pile. At what rate is the diameter of the pile
changing when the pile is 12 feet high?

Show steps please!

Thank you!

  1. 👍 0
  2. 👎 0
  3. 👁 231
  1. let the height be h
    then the diameter of the base is 4h, thus the radius is 2h

    given: dV = 20 ft^3/min
    find: d(2h)/dt , when h = 12

    V = (1/3)π r^2 h
    = (1/3) π (4h^2)(h)
    = (4/3) π h^3

    dV/dt = 4π h^2 dh/dt
    20 = 4π((144) dh/dt
    dh/dt = 5/(144π)
    so
    d(2h)/dt = 10/(144π)
    = 5/(72π)
    = appr .0221 ft/min

    1. 👍 0
    2. 👎 0
  2. I was just reading the last solution and I was wondering why he had the 1/3 before the pir^2h.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Science HELP

    Sodium is a metal and chlorine is a poisonous gas. Neither is safe to eat. However, when sodium and chlorine combine, it produces edible table salt. What can be concluded? A. Table salt has similar physical properties of both

  2. chemistry

    a hydrated salt is a solid that includes water molecules within its crystal structure. a student heated a 9.10-gram sample of a hydrated salt to a constant mass of 5.41 grams. what percent by mass of water did the salt contain?

  3. chemistry

    A pan full of hot salt water, NaCl(aq), is cooled and NaCl(s) precipitates. Explain why this happens. Chloride ions are more strongly attracted to the metal in the pan than the sodium ions at low temperatures. As the vapor

  4. AP CHEMISTRY

    An unknown salt is either KBr, NH4Cl, KCN, or K2CO3. If a 0.100 M solution of the salt is neutral, what is the identity of the salt?

  1. Math

    The city highway department bought 3/4 tons of salt to put on the road when it snows. They have used 2/7 of salt. How many tons has the city highway department used?

  2. Chemistry

    an unknown salt is either NaCN,NaC2H3O2, NaF, NaCl, or NaOCl. when 0.100 molar of the salt is dissolved in 1.00 L of solution, the ph of the solution is 8.07. what is the identity of the salt? where do I start? How do I solve it,

  3. Chemistry

    What happens to the sample's reported water content if the salt decomposes yielding a volatile product? If the water is not completely removed from the salt during the heating process, will the reported water-to-salt mole ratio be

  4. science

    A beaker contains a mixture of sand and salt. A student adds water to dissolve the salt. Which processes can be used to separate out the sand and salt? distillation to collect the sand and filtration to collect the salt

  1. Geometry

    An hourglass, composed of two identical cones, is 12 cm tall. The radius of each cone is 3 cm. If you want to fill the bottom half of the hourglass 2/3 full of salt, how much salt will you need? Explain the method you would use to

  2. Science~!

    Sodium is a metal and chlorine is a poisonous gas. Neither is safe to eat. However, when sodium and chlorine combine, it produces edible table salt. What can be concluded? (1 point) Table salt has similar physical properties of

  3. science

    A beaker contains a mixture of sand and salt. A student adds water to dissolve the salt. Which processes can be used to separate out the sand and salt? distillation to collect the sand and filtration to collect the salt

  4. Science 6TH Grade

    Salim added 1 g of salt to each of four beakers filled with water. He stirred the water at different speeds, and recorded how long it took for the salt to dissolved. Stirring - Time (sec) No stirring - 25 Slow stirring - 18 Medium

You can view more similar questions or ask a new question.