i need help with this word problem

kaebun

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Sep 11, 2005
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A high-altitude sperical weather balloon expands as it rises due to the drop in atmospheric preasure. Suppose that the radious r increases at the rate of 0.03 inch per second and that r=48 inchs at t=0 determine an equation that models the volume V of the bllon at time and find the volume when t=300 seconds
 
volume of a sphere,V, equals 4/3 pi r^3 r is radius

V(t)= 4/3 pi [ r(t)]^3

but dr/dt = .03 integrate
r=.03t+c at t=0 r=48
48=0+c
c=48
r(t)= .03t+48

V(t)= 4/3 pi [.03t+48]^3 inchs cubed t>0

let t=300 to find V at 300 secs
 
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