related rates calculus problem

posted by .

A balloon is being filled with air at a rate of 3 cubic meters per minute. Find the rate at which the radius is changing when the volume is 113.0973355 cubic meters.

  • related rates calculus problem -

    V = (4/3)πr^3
    dV/dt = 4πr^2 dr/dt

    we know dV/dt, but we have to find r

    113.0973355 = (4/3)πr^3 , ( I am sure they gave you that number as 36π)
    r^3 = 27
    r = 3

    subbing in
    3 = 4π9) dr/dt
    dr/dt = 1/(3π) m/min

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Related Rates

    Water is leaking out of an inverted conical tank at a rate of 500 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 10 meters and the diameter at the top is …
  2. calc

    hydrogen is being pumped into a spherical balloon at the rate of 250 cubic inches per minute. in a and b, you must provide an equation with their proper numerical factors when showing the relationships inquired A) write an equation …
  3. calculus

    You are letting the air out of a hot air balloon at a steady rate. The volume of the balloon is decreasing at the rate of 10pi m^3/min when the diameter is 45 meters. At what rate is the radius of the balloon changing?
  4. AP calculus AB

    A balloon is being filled with air at a rate of 3 cubic meters per minute. Find the rate at which the radius is changing when the volume is 36 pi cubic meters.
  5. related rates problem-calculus

    A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi …
  6. calculus(related rates)

    Water is leaking out of an inverted conical tank at a rate of 12200 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 15 meters and the diameter at the top …
  7. relaited rates

    A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meter per minute.At what rate is the radius increasing when the radius is 6 meters?
  8. calculus

    a spherical balloon filled with gas has a leak that permits the gas to escape at a rate of 1.5 cubic meters per minute. how fast is the surface area of the balloon shrinking when the radius is 4 meters?
  9. Math - Related Rates

    Air is being pumped into a spherical balloon at a rate of 2 cubic meters per minute. At what rate is the radius changing when the volume of the balloon is 36pi cubic meters?
  10. calculus

    A spherical balloon , initially inflated to a volume of over 30000 cubic meters, springs a leak which causes the radius to decrease at a rate of 2 meters per minute. At the instant when the radius is 3 meters , how fast ( in cubic …

More Similar Questions