Multiple choice

What is the ratio of the areas of the incircle and the circumcircle of a square of side 10 cm?

  1. 1 : 1

  2. 1 : 2

  3. 2 : 1

  4. 3 : 1

  5. 1 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a square of side 10 cm, the incircle radius is 5 cm and the circumcircle radius is 5*sqrt(2) cm. The ratio of areas is (pi*5^2) / (pi*(5*sqrt(2))^2) = 25 / 50 = 1/2.

AI explanation

For a square of side 10 cm, the diameter of its incircle is 10 cm, meaning its radius is 5 cm. The diameter of the square's circumcircle is equal to the diagonal of the square, which is 10 root 2 cm, making its radius 5 root 2 cm. Using the area of a circle formula, the area of the incircle is pi times 5 squared, which is 25 pi, and the area of the circumcircle is pi times (5 root 2) squared, which is 50 pi. The required ratio of their areas is 25 pi is to 50 pi, which simplifies to 1 is to 2.

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