Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. dA dt = dr dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 25 m?
Area of the circle A = πr²
dA/dr = 2πr where r is the radius of the circle
dA/dt = dA/dr * dr/dt
dr/dt is the rate of increase in radius of the oil spill.
Given
dr/dt = 1m/s
radius r = 25m
Substitute into the formula above;
dA/dt = dA/dr * dr/dt
dA/dt = 2πr * 1
dA/dt = 2π(25) * 1
dA/dt = 50πm²/s
dA/dt = 157.1m²/s
Hence the area of the spill is increasing at the rate of 157.1m²/s
