Multiple choice

The side of a square is 10 cm. Find the ratio of area of circumscribed and inscribed circles. एक वर्ग की भुजा 10 सेमी हैं। इसके परिवृत्त और अन्तः वृत्त के क्षेत्रफल का अनुपात ज्ञात कीजिए।

  1. 1:2

  2. 2:1

  3. 2:3

  4. 3:2
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B Correct answer
Explanation

For square with side 10 cm, circumscribed circle has diameter = diagonal = 10√2 cm, so radius = 5√2 cm. Area = π(5√2)² = 50π. Inscribed circle has diameter = side = 10 cm, so radius = 5 cm. Area = π(5)² = 25π. Ratio of areas = 50π : 25π = 2:1. The circumscribed circle always has twice the area of the inscribed circle for a square.

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