What is the area of the segment formed by a chord in a circle of radius 10 cm, if the angle subtended at the center is 90\(^\circ\) ?
What is the area of the segment formed by a chord in a circle of radius 10 cm, if the angle subtended at the center is 90\(^\circ\) ?
10 सेमी त्रिज्या वाले वृत्त में एक जीवा द्वारा बनाए गए रेखाखंड का क्षेत्रफल क्या है, यदि केंद्र पर अंतरित कोण 90\(^\circ\) है?
Detailed Solution & Logic
Correct Answer:
\(25\pi - 50\)
Radius of circle r = 10 cm, Central angle $ \theta = 90^\circ$
Area of sector = $ \frac{\theta}{360} \pi r^2 = \frac{90}{360} \pi (10)^2 = 25\pi$
Area of triangle inside sector = $ \frac{1}{2} \times 10 \times 10 = 50$
Area of segment = Area of sector - Area of triangle = $ 25\pi - 50$
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