Answer :
The rate of change of the area at the instant the radius is 10 ft is 376.99 ft² / min.
The rate of change describes how one quantity changes in relation to the change in another quantity.
If a circle has an initial radius of 50 ft and decreases at a rate of 2 ft/min, then the time it took the radius to become 10 ft is 20 min.
r = r₀ - (rate)(time)
10 ft = 50 ft - (2 ft/min)(time)
(2 ft/min)(time) = 40 ft
time = 20 min
Solve the rate of change in area by dividing the change in area after time = 20 min.
rate of change = change in area / change in time
rate of change = A(r = 50) - A(r = 10) / 20 min
rate of change = π(50² - 10²) / 20 mins
rate of change = 376.99 ft² / min
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