# calculus

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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

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