Multiple choice

A circle circumscribe a rectangle with side 15 cm and 8 cm. What is the area of the circle एक वृत्त में एक आयत खींचा गया है, जिसकी भुजाएं 15 सेमी और 8 सेमी है। वृत्त का क्षेत्रफल है।

  1. 48 π sq. cm./वर्ग सेमी.

  2. 100 π sq. cm./वर्ग सेमी.

  3. 72.25 π sq. cm./वर्ग सेमी.

  4. 200 π sq. cm./वर्ग सेमी.
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C Correct answer
Explanation

When a rectangle is circumscribed by a circle, the diagonal of the rectangle equals the diameter of the circle. Diagonal = √(15² + 8²) = √(225 + 64) = √289 = 17 cm. Radius = diagonal/2 = 8.5 cm. Area of circle = πr² = π(8.5)² = π × 72.25 = 72.25π sq. cm.

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