Multiple choice

Circumference of a circle is $S$ cm. and its area is $A: cm^2$. Which one of the following relations is true?

  1. $\pi S^2 > 4A$
  2. $S^2 < 2\pi A$
  3. $S = 4\pi A$
  4. $S^2 = 4\pi A$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

S = 2 * pi * r, so r = S / (2 * pi). A = pi * r^2 = pi * (S / (2 * pi))^2 = pi * S^2 / (4 * pi^2) = S^2 / (4 * pi). Thus, 4 * pi * A = S^2.

AI explanation

The circumference of the circle is given as S, which means the radius is S divided by 2pi. The area A is calculated using the formula A = pi * r^2, which substitutes to A = pi * (S / 2pi)^2. Simplifying this expression yields A = S^2 / (4pi). Multiplying both sides by 4pi gives the correct relation S^2 = 4piA.

Keep practicing — related questions