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?

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:

\pi(R^2-r^2)

Area of outer circle:

\pi R^2

Therefore,

\text{Required Ratio} = \frac{\pi(R^2-r^2)}{\pi R^2} = \frac{R^2-r^2}{R^2}

Substituting $R=10$ and $r=7$ :

(10^2-7^2):10^2

=(100-49):100

=51:100

Approximate ratio:

51:100 \approx 50:100

=1:2

Alternative Method / वैकल्पिक विधि

Ring area:

\pi(100-49)=51\pi

Outer circle area:

100\pi

Ratio:

51\pi:100\pi = 51:100 \approx 1:2

Final Answer / अंतिम उत्तर

\boxed{1:2}

✅ Correct Answer / सही उत्तर: 1 : 2

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