A tanker is spilling oil into the Gulf of Mexico resultin in an oil slick that is close to circular in shape. At he time the slick's diameter is growing at the rate of 4 ft^2/min, the diameter is 500 feet. At what rate is the area of the oil slick spreading?
Answers: (a) 12566.4 ft^2/min (b) 3141.6 ft^2/min
(c) 1570.8 ft^2/min (d) 4000pi ft^2/minWill someone help me solve this Calculus problem regarding the area of the oil slick spreading?
A = 蟺 r虏
dA/dt = dA/dr dr/dt ................... chain rule
= 2蟺r dr/dt .............................. dr/dt given as 4/2 ft/min
= 2蟺 (500/2) (4/2)
= 1000蟺 ft虏/min
Answer: dA/dt 鈮?3141.6 ft虏/minWill someone help me solve this Calculus problem regarding the area of the oil slick spreading?
the area of a circle =(pi d^2) /4
hence A=(pid^2)4
differentiating A with respect to time gives
dA/dt=(0.5dpi)dD/dt where D is the diameter
putting the values given to find dA/dt, then it follows that
dA/dt= 0.5*3.1416*500*4
=3141.6ft^2/min
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