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 4/3πr3. the surface area is 4πr2. set up the differential equation for how r is changing. then, suppose that at time t = 0 minutes, the radius is 10 centimeters. after 5 minutes, the radius is 8 centimeters. at what time t will the snowball be completely melted.

According to the passage, we have the next equation:

where "K" is a proportional constant

Leaving at the end with the next equation:

Integrating the equation, we have:

where "C" is a constant

Then, we have the 2 conditions for the problem:

1) t=0 → r=10

Replacing in the equation, we have C = 10

2) t=5 → r=8

Replacing in the equation, we have K = -0.4

Finally, the time which the snowball will be completely melted will be when r = 0. So replacing in the equation

t = 25 minutes

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step-by-step explanation: