The inner and outer diameter of a ring is 14 cm and 28 cm respectively. What is the area of ring?

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RRB NTPC Exam 20 Jan 2021 click here to view all questions

The inner and outer diameter of a ring is 14 cm and 28 cm respectively. What is the area of ring?

A528 cm²

B484 cm²

C462 cm²

D506 cm²

Akhilesh ? Apr 7 '25 at 21:46

correct answer is: option c : 462 cm²
Explanation: The area of a ring is the difference between the area of the outer circle and the area of the inner circle. The formula for the area of a circle is \(`\pi r^2`\), where `r` is the radius.

We are given the inner diameter as 14 cm, so the inner radius is 14/2 = 7 cm.

We are given the outer diameter as 28 cm, so the outer radius is 28/2 = 14 cm.

The area of the outer circle is \(`\pi (14)^2 = 196\pi`\).

The area of the inner circle is \(`\pi (7)^2 = 49\pi`\).

The area of the ring is \(`196\pi - 49\pi = 147\pi`\). Using \(`\pi \approx \frac{22}{7}`\), the area is \(`147 \times \frac{22}{7} = 21 \times 22 = 462`\) cm².

• Option a: 528 cm² is incorrect. This likely arises from an error in calculating the radii or applying the area formula.
• Option b: 484 cm² is incorrect. This likely arises from an error in calculating the radii or applying the area formula.
• Option c: 462 cm² is the correct area of the ring, calculated as \(`\pi (14^2 - 7^2)`\).
• Option d: 506 cm² is incorrect. This likely arises from an error in calculating the radii or applying the area formula.

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correct answer is: option c : 462 cm² Explanation: The area of a ring is the difference between the area of the outer circle and the area of the inner circle. The formula for the area of a circle is \(`\pi r^2`\), where `r` is the radius. We are given the inner diameter as 14 cm, so the inner radius is 14/2 = 7 cm. We are given the outer diameter as 28 cm, so the outer radius is 28/2 = 14 cm. The area of the outer circle is \(`\pi (14)^2 = 196\pi`\). The area of the inner circle is \(`\pi (7)^2 = 49\pi`\). The area of the ring is \(`196\pi - 49\pi = 147\pi`\). Using \(`\pi \approx \frac{22}{7}`\), the area is \(`147 \times \frac{22}{7} = 21 \times 22 = 462`\) cm². Option a: 528 cm² is incorrect. This likely arises from an error in calculating the radii or applying the area formula. Option b: 484 cm² is incorrect. This likely arises from an error in calculating the radii or applying the area formula. Option c: 462 cm² is the correct area of the ring, calculated as \(`\pi (14^2 - 7^2)`\). Option d: 506 cm² is incorrect. This likely arises from an error in calculating the radii or applying the area formula. Akhilesh ? answered Apr 7 '25 at 21:46

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