A ring-shaped disc has outer radius 10 cm and inner radius 7 cm. What is the approximate ratio of the ring's area to the whole outer circle?
एक वलयाकार (Ring-shaped) डिस्क की बाहरी त्रिज्या 10 सेमी और आंतरिक त्रिज्या 7 सेमी है। वलय के क्षेत्रफल और पूरे बाहरी वृत्त के क्षेत्रफल का लगभग अनुपात क्या होगा?
Options / विकल्प
- A. 1 : 2 ✅
- B. 2 : 3
- C. 3 : 4
- D. 4 : 5
Answer / उत्तर
1 : 2
Solution / समाधान
Shortcut Trick / शॉर्टकट ट्रिक
Area of ring: π(R2 − r2)
Area of outer circle: πR2
Therefore, Required Ratio =
π(R2 − r2) / πR2 = (R2 − r2) / R2
Substituting R = 10 and r = 7:
(102 − 72) : 102 = (100 − 49) : 100 = 51 : 100
Approximate ratio: 51 : 100 ≈ 50 : 100 = 1 : 2
Alternative Method / वैकल्पिक विधि
Ring area = π(100 − 49) = 51π
Outer circle area = 100π
Ratio = 51π : 100π = 51 : 100 ≈ 1 : 2
Final Answer / अंतिम उत्तर
1 : 2
Quick Revision / Key Points
- The area of a ring-shaped disc is the difference between the areas of the outer and inner circles.
- Formula for ring area: π(R2 − r2), where R is outer radius and r is inner radius.
- The ratio of the ring's area to the whole outer circle's area simplifies to (R2 − r2) / R2.
- For R = 10 cm and r = 7 cm, the ratio is approximately 1 : 2.
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