(a) 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. Below, use "s" for 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 1m/s, how fast must the area of the spill increasing when the radius is 27m?

Question

(a) 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. Below, use "s" for 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 1m/s, how fast must the area of the spill increasing when the radius is 27m?

anonymous · Answer

i found the answer for a) 2*pi*r*s
but for b i keep getting the wrong answer i keep getting 169.65

phi · Answer

maybe they want the answer in terms of pi?
$$ 54\pi \frac{m^2}{sec} $$

anonymous · Answer

ok ill try that

anonymous · Answer

that worked how did you get your answer in pi

phi · Answer

instead of multiplying out using pi= 3.14159...  you leave it pi
so
2*pi*27*1  becomes  54*pi  or $54\pi$

anonymous · Answer

oh ok that makes sense that thanks for explaining