Burhan Hopper

2021-01-02

The rate of change of the volume of a snowball that is melting is proportional to the surface area of the snowball. Suppose the snowball is perfectly spherical. Then the volume (in centimeters cubed) of a ball of radius r centimeters is

Daphne Broadhurst

Skilled2021-01-03Added 109 answers

Step 1

Given:

The rate of change of the volume of a snowball that is melting is proportional to the surface area of the snowball is perfectly spherical

Then the volume (in centimetres cubed) of a ball of radius r centimetres is

And the surface area is

Set up the differential equation for how r is changing.

Then, suppose that at time t=0 minutes,the radius is 10 centimetres.After 5 minutes,the radius is 8 centimetres

Step 2

To find: At the what time t will be snowball be completely melted?

From the given conditions ,

By putting this value in (1)

The equation must be,

Now,

so,

c=10 and here

After the 5 minutes,

Now equation (2)becomes,

This shows the differential equation for how r is changing.

As the snowball completely melted that means the radius of the snowball is zero.

From this by substituting

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