Answer:
2260.8 ft ^ 2 / s
Step-by-step explanation:
To solve the problem we first know that:
dr / dt = 6 ft / s
r = 60 ft
Now they ask us for dA / dt, the change of the area with respect to time, by chain rule we have to:
dA / dt = dA / dr * dr / dt
we have that A = pi * r ^ 2
d (pi * r ^ 2) / dr
deriving the above we are left with:
2 * pi * r
replacing:
dA / dt = (2 * pi * r) * 6
dA / dt = 2 * 3.14 * 60 * 6
dA / dt = 2260.8 ft ^ 2 / s
therefore the area change per second is 2260.8 ft ^ 2 / s