SOLUTION: A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.03in./sec and that r = 4

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Question 151280: A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.03in./sec and that r = 48in. at time t = 0; Determine an equation that models the volume v of the balloon at time t, and find the volume v of the balloon at time t, and find the volume when t = 300 sec

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.03in./sec and that r = 48in. at time t = 0; Determine an equation that models the volume v of the balloon at time t, and find the volume v of the balloon at time t, and find the volume when t = 300 sec
:
Volume of a sphere: V = %284%2F3%29pi%2Ar%5E3
:
Volume when the balloon is launched (t=0):
V = %284%2F3%29pi%2A48%5E3
V = 463,246.7 cu inches
:
The equation for this problem: t = time in seconds
V = %284%2F3%29pi%2A%2848%2B.03t%29%5E3
:
For t = 300
V = %284%2F3%29pi%2A%2848%2B.03%2A300%29%5E3
V = %284%2F3%29pi%2A%2848%2B9%29%5E3
V = %284%2F3%29pi%2A57%5E3
V = 775,734.6 cu inches after 300 sec