Multiple choice

The area of the circle inscribed in a square of side $a$, is $a^2cm^2$. With justification, state whether the statement is:

  1. true, since the radius of the circle is $\cfrac{a}{2}$
  2. false, since the radius of the circle is $\cfrac{a}{2}$
  3. true, since the radius of the circle is $\cfrac{a}{4}$
  4. false, since the radius of the circle is $\cfrac{a}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A circle inscribed in a square of side a has a diameter equal to a, so its radius is a/2. The area of this circle is pi * (a/2)^2 = pi * a^2 / 4, which is not a^2.

AI explanation

When a circle is inscribed in a square, the diameter of the circle equals the side length of the square. Therefore, the radius is a/2. Applying the area of a circle formula, Area = pi * r^2 = pi * (a/2)^2 = pi*a^2 / 4. Since pi*a^2 / 4 is not equal to a^2, the given statement is false, and the radius is a/2. The correct option is B.

Keep practicing — related questions