Multiple choice

Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circle. If remaining area of the square is 94.5 cm2, what is the radius of the circle? (in cm.) एक वर्ग के चार कोनों पर केंद्रों के साथ समान त्रिज्या वाले चार वृत्त बनाये जाते हैं। प्रत्येक वृत्त अन्य दो आसन्न वृत्तों को स्पर्श करता है। यदि वर्ग का शेष क्षेत्रफल 94.5 सेमी2 है, तो वृत्त की त्रिज्या क्या है? (सेमी में)

  1. 10

  2. 7

  3. 10.5

  4. 3.5

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The square has side 2r since circles at adjacent corners touch. Square area = 4r². Four quarter-circles at corners form one full circle of area πr². Remaining area = 4r² - πr² = r²(4 - π) = 94.5. Solving: r² = 94.5/(4 - π) ≈ 110.1, so r ≈ 10.5 cm.

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