calculus

posted by .

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.

  • calculus -

    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
    so
    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

  • calculus -

    can you solve it with separation of differential equation

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. MATH: Functions

    The radius, r, in centimeters, of a melting snowball is given by r=50-2.5t, where t is time in hours. the snowball is spherical, with volume V=4/3(pi)r^3 cm^3. Find a formula for V=f(t), the volume of the snowball as a function of …
  2. 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)
  3. Calculus

    A certain calculus student hit Mrs. Evans in the head with a snowball. If the snowball is melting at the rate of 10 cubic feet per minute, at what rate is the radius of the snowball changing when the snowball is 1 foot in radius?
  4. Calculus

    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 …
  5. calculus

    A spherical snowball is placed in the sun. The snowball melts so that it's surface area decreases at a rate of 2 cm2 /min. Find the rate at which the diameter decreases when the diameter is 8 cm
  6. Calc

    A spherical snowball is placed in the sun. The snowball melts so that it's surface area decreases at a rate of 2 cm2 /min. Find the rate at which the diameter decreases when the diameter is 8 cm. I'm not sure what formulas to use, …
  7. Advanced Algebra

    The volume V (r) of a sphere is a function of its radius r. Suppose a spherical snowball with a radius 2 f t started to melt so that the radius is changing at a constant rate of 4.5 inches per minute. If f(t) feet is the radius of …
  8. Calculus

    A snowball melts at a rate of 2 cubic inch an hour. When the volume is 36π in^3, how fast is the radius shrinking?
  9. math

    While building a snowman, a large snowball is created at the rate of 5 inches per hour. How fast is the volume of the snowball changing at the instant the snowball has a radius of 10 inches?
  10. 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 there …

More Similar Questions