Question
Download Solution PDFनिम्नलिखित चित्र में, चाप AB की लंबाई वृत्त की त्रिज्या r के पाँच गुना के बराबर है। त्रिज्यखंड AOB का क्षेत्रफल ज्ञात कीजिए?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFचाप AB की लंबाई वृत्त की त्रिज्या r के पाँच गुना के बराबर है।
प्रयुक्त सूत्र:-
त्रिज्यखंड का क्षेत्रफल = (θ/360) × πr²
चाप की लंबाई = (θ/360) × 2πr
जहाँ,
θ डिग्री में केंद्रीय कोण है।
r वृत्त की त्रिज्या है।
गणना:-
चाप AB की लंबाई त्रिज्या के पाँच गुना के बराबर है,
⇒ 5r = (θ/360) × 2πr
⇒ θ = (5r × 360) / (2πr)
θ = 900 /π डिग्री
त्रिज्यखंड का क्षेत्रफल = (900/(360× π )) × πr²
त्रिज्यखंड का क्षेत्रफल = 2.5r²
∴ त्रिज्यखंड AOB का क्षेत्रफल 2.5r2 है।
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