Post a New Question

Calculus

posted by .

A right circular cone has a constant volume. The height h and the base radius r can both vary. Find the rate at which h is changing with respect to r at the instant when r and h are equal.

  • Calculus -

    v = pi/3 r^2 h

    since v is a constant, dv = 0

    0 = 2rh dr + r^2 dh

    When r=h,

    2r^2 dr + r^2 dh = 0
    2dr + dh = 0

    dh = -2dr

    dh/dr = -2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. AP Calculus..again

    A balloon is composed of a right circular cone joined at its base to a hemisphere. The diameter of the base is equal to the height of the cone. If the balloon is inflated, at what rate is the volume, V, changing with respect to the …
  2. calculus

    oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute. The oil slick takes the form of a right circular cylinder with both its …
  3. math

    Resolved QuestionShow me another » AP Calculus related rates problem?
  4. Calculus AB

    The volume V or a cone (V = 1/3 π r² h) is increasing at a rate of 28π cubic units per second. At the instant when the radius r of the cone is 3 units, its volume is 12π cubic units and the radius is increasing at 0.5 …
  5. Calculus

    Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have …
  6. Calculus

    Let V be the volume of a right circular cone having height h and radius r and assume that h and r vary with time. a. Express the time rate of change of the cylinder in terms of h, r and their rates of change. b. At a certain instant, …
  7. math

    Two right circular cone, one upside down in the other. The two bases are parallel. The vertex of the smaller cone lies at the center of the larger cone’s base. The larger cone’s height and base radius are 12 and 16 ft, respectively. …
  8. Calculus

    Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing …
  9. calculus

    the volume V of a right circular cone of height h=8 feet and radius r feet is V=V(r)=2pier^2. If r is changing, find the instantaneous rate of change of the volume V with respect to the radius r at r=4.
  10. Calculus: Optimization

    I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance. Given a right circular cone, you put an upside-down cone …

More Similar Questions

Post a New Question