Calculus- rates

A tanker is spilling oil into the water resulting in an oil slick that is close to circular. At te time that the slick's diameter is growing at a rate of 8 ft/sec, the diameter is 250 feet. At what rate is the area of the oil sick increasing?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. area = A = pi r^2
    dA/dr = 2 pi r
    dA/dt = 2 pi r dr/dt
    which we did not really have to do because obviously the rate of change of area is the rate of change of radius times the circumference.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trig(I think)

    Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1m/s, how fast is the area of the spill increasing when the radius is 30m?

  2. Math

    Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of

  3. Physics

    1. A cylindrical disk of wood weighing 45.0N and having a diameter of 30.0 cm floats on a cylinder of oil of density 0.850 g/cm3. The cylinder of oil is 75.0 cm deep and has the same diameter of the wood. (a) What is the gauge

  4. history

    Which describes the relationship between oil-producing Middle Eastern nations and the consumer states that consume their petroleum? Consumer states often are dependent on Mideast oil producers, but potential ties to terrorist

  1. CALCULUS

    A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius of the slick is expanding at 0.1 m/min, and its thickness is .02 m. At that moment: a. How fast is the area

  2. 4 Calculus Related-Rates Problems

    1. How fast does the radius of a spherical soap bubble change when you blow air into it at the rate of 15 cubic centimeters per second? Our known rate is dV/dt, the change in volume with respect to time, which is 15 cubic

  3. Social studies

    Oil is important to Iran’s economy because _________________. A. Oil purchases are the country's greatest expense. B. Oil sales are a major part of the country's income.*** C. Oil spill have meant expensive environmental

  4. CAL-Help on dr/dt

    A circular oil slick of uniform thickness is caused by a spill of 1 cubic meter of oil. The thickness of the oil is decreasing at the rate of 0.1 cm/hr as the slick spreads. (Note: 1 cm = 0.01 m.) At what rate is the radius of the

  1. Calculus

    An oil tank in the shape of a right circular cylinder, with height 30 meters and a radius of 5 meters is two-thirds full of oil. How much work is required to pump all of the oil over the top of the tank? (The density of oil is 820

  2. math

    The radius of a circular oil slick expands at a rate of 8 m/min. a. How fast is the area of the oil slick increasing when the radius is 30 m? = 480pi b.If the radius is 0 at time t=0 , how fast is the area increasing after 2 mins?

  3. Calculus

    Oil is leaking out of a ruptured tanker at a rate of r = 19e^(2t) gallons per hour. Write a definite integral that represents the total quantity of oil which leaks out of the tanker in the first 3 hours. Using your formula answer

  4. Chemistry

    The reason that nonpolar oil will not dissolve in polar water is that the attractive forces between: A. the oil molecules are ionic and the attractive forces between the water molecules are covalent. B. the water molecules are

View more similar questions or ask a new question.