Multiple choice

If P represents the area and W represents the circumference of the circle then P in terms of W is

  1. $\displaystyle \frac{2\pi }{W}$
  2. $\displaystyle \frac{4\pi^{2} }{W}$
  3. $\displaystyle \frac{2\pi^{2} }{W}$
  4. $\displaystyle \frac{W^{2} }{4\pi }$
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D Correct answer
Explanation

Area P = pi * r^2. Circumference W = 2 * pi * r, so r = W / (2 * pi). Substituting r into P: P = pi * (W / (2 * pi))^2 = pi * (W^2 / (4 * pi^2)) = W^2 / (4 * pi).

AI explanation

The circumference formula is W equals 2 pi r, so the radius r equals W divided by 2 pi. Substituting this into the area formula, P equals pi r squared, gives P equals pi times the square of W divided by 2 pi. This simplifies to W squared divided by 4 pi.

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