A snowball has a radius of 3 inches. Assume the rate with which the volume of the snowball melts is proportional to its surface area. If, after 1 hour, the radius of the snowball is 2.9 inches, predict what the radius will be after one day.

  1. 👍
  2. 👎
  3. 👁
  1. dv/dt = k (4 pi r^2) given

    v = (4/3) pi r^3 geometry
    dv/dr = 4 pi r^2
    dv/dt = dv/dr dr/dt = 4 pi r^2 dr/dt
    k is dr/dt which is constant
    dr/dt = (2.9 - 3)/1 = -0.1 in/hr

    starts at 3 in
    r = 3 - .1(24) = 3-2.4 = 0.6 inches

    1. 👍
    2. 👎
  2. can you solve it with separation of differential equation

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100pi square inches, what is the rate of increase, in cubic inches per second, in the volume V?

  2. Algebra

    The cone shown has a height of 5 inches and a radius of 1.5 inches. What is the approximate volume of the cone? A. Between 11 and 12 cubic inches B. Between 15 and 16 cubic inches C. Between 35 and 36 cubic inches D. Between 39

  3. calculus

    A spherical balloon is losing air at the rate of 2 cubic inches per minute. How fast is the radius of the ballon shrinking when the radius is 8 inches.

  4. calculus

    3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of

  1. Geometry/Math

    Two right circular cylinders have equal volume. The first cylinder has a radius of 6 inches and a height of 12 inches. What is the number of inches in the height of the second cylinder if its radius is 8 inches? Express your

  2. Calculus

    A storage tank used to hold sand is leaking. The sand forms a conical pile whose height is twice the radius of the base. The radius of the pile increases at the rate of 2 inches per minute. Find the rate of change of volume when

  3. algebra

    volume of cone varies jointly as square of its radius and its height if volume of a cone is 27pie cubic inches when radius is 3 inches and height is 9 inches find volume of a cone when radius is 4 inches and height is 3 inches

  4. calculus

    A snowball is melting at the rate of 2 inches per hour. How fast is the surface area of the snowball changing at the instant the snowball has a radius of 3 inches i tried (d/dt) = 4pir^2 (dr/dt) its multiple choice and -72pi isnt

  1. math

    The volume V of a sphere of radius r is given by the formula V (r) = (4/3)πr^3. A balloon in the shape of a sphere is being inflated with gas. Assume that the radius of the balloon is increasing at the constant rate of 2 inches

  2. physics

    One strategy in a snowball fight is to throw a snowball at a high angle over level ground. While your opponent is watching the first one, a second snowball is thrown at a low angle timed to arrive before or at the same time as the

  3. math

    A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 9 cm.

  4. calculus

    Melting Snowball: A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant. (Hint: Surface Area =4(pi)r^2)

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