Calculus

posted by .

A block of ice is exposed to heat in such a way that the block maintains a similar shape as it metls. The block of ice is initially 2' wide, 2 'high, and 3' long. If the change in the width of the ice is -1/3 ft/hr, find: the amount of time it will tak efor the block of the ice to completely melt.

I found that the rate of change in the volume of the ice block is -3/2 ft^3/hr. Do you just divide the volume of the cube (12 ft^3) by the rate of change of the volume (-3/2 ft^3/hr)?

  • Calculus -

    v = w*w*3w/2 = 3/2 w^3
    dv/dt = 9/2 w^2 dw/dt
    = 9/2 * -1/3 = -3/2

    your dv/dt is correct.

    as for your question, consider the units:

    time = ft^3 / ft^3/hr = 12/(3/2) = 8 hr

  • Calculus -

    Thank you! That was helpful :)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics B

    A 40-kg block of ice at 0°C is sliding on a horizontal surface. The initial speed of the ice is 7.0 m/s and the final speed is 4.7 m/s. Assume that the part of the block that melts has a very small mass and that all the heat generated …
  2. physics

    A block of ice at 0°C whose mass initially is m = 12.5 kg slides along a horizontal surface, starting at a speed vo = 4.10 m/s and finally coming to rest after traveling a distance d = 10.07 m. Compute the mass of ice melted as a …
  3. physics

    A rectangular block of ice 8 m on each side and 1.5 m thick floats in sea water. The density of the sea water is 1025 kg/m3. The density of ice is 917 kg/m3. a) How high does the top of the ice block float above the water level?
  4. physics

    A rectangular block of ice 10 m on each side and 1.1 m thick floats in sea water. The density of the sea water is 1025 kg/m3. The density of ice is 917 kg/m3. a) How high does the top of the ice block float above the water level?
  5. physics

    A rectangular block of ice 10 m on each side and 1.1 m thick floats in sea water. The density of the sea water is 1025 kg/m3. The density of ice is 917 kg/m3. a) How high does the top of the ice block float above the water level?
  6. physics

    A 1.3- block of ice is initially at a temperature of -3.5. If 6.6×105 of heat are added to the ice, what is the final temperature of the system?
  7. physics

    A 40-kg block of ice at 0°C is sliding on a horizontal surface. The initial speed of the ice is 7.0 m/s and the final speed is 4.7 m/s. Assume that the part of the block that melts has a very small mass and that all the heat generated …
  8. physics

    A block of ice at 0°C whose mass initially is m = 48.4 kg slides along a horizontal surface, starting at a speed vo = 4.91 m/s and finally coming to rest after traveling a distance d = 12.28 m. Compute the mass of ice melted as a …
  9. physics

    an ice skater applies a horizontal force to a 20 kg block on frictionless, level ice causing the block to accelerate uniformly at 1.4 m/s^2 to the right. after the skater stops pushing the block it slides onto a region of ice that …
  10. physic

    c. A 2 kg block of ice has been stored in a chiller at a constant 0°C. In order to carry out an investigation, the block of ice needs to be turned into water at a temperature of 75°C. Calculate how much heat energy is required to …

More Similar Questions