Ahigh-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 0.07 inches per second, and that r = 36 inches at time t = 0. determine the equation that models the volume v of the balloon at time t, and find the volume when t = 400 seconds.

1098066.2 cubic inches

Step-by-step explanation:

When time(t) = 0, radius of spherical weather balloon(r) = 36 inches

Since, the radius increases at 0.07 inches per second. Hence, the radius of the balloon after t=0 will be, r(t) = 36+0.07t

Now the volume of sphere (V) = \frac{4}{3}\pi r^3

                                               V(t)    = \frac{4}{3}\pi (36+0.07t)^3

We need to calculate volume when t = 400 seconds

V(400) = \frac{4}{3}\pi (36+0.07*(400))^3

           =  4/3*pi*(64)^3

           = 1098066.2 cubic inches  

23

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