The volume of a spherical hot air balloon v(r) = 4 3 πr3 changes as its radius changes. the radius is a function of time given by r(t) = 3t. find the average rate of change of the volume with respect to t as t changes from t = 1 to t = 4.

we are given

volume of sphere as

(a)

we can plug r into V

we get

(b)

we can use average rate of change formula

here , we are given t=1 to t=4

so, we get formula as

now, we can plug values

.............Answer

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step-by-step explanation: