The area of two concentric circles is 962.5 cm2 and 1386 cm2. Find the width of the ring made by them.

Correct option is D

Given:

Area of the larger circle = 1386 cm²
Area of the smaller circle = 962.5 cm²

Formula Used:

1. Area of a circle:
​$$A = \pi r^2$$​
For the two circles:
​$$A_1 = \pi R^2 \quad \text{and} \quad A_2 = \pi r^2$$​
where R is the radius of the larger circle, and r is the radius of the smaller circle.

2. The width of the ring is the difference between the radii:
Width = R - r

Solution:

1. Calculate the radii using the area formula:
​$$R^2 = \frac{A_1}{\pi} = \frac{1386}{3.1416} \approx 441 \quad \Rightarrow \quad R = \sqrt{441} = 21 \, \text{cm}$$​
​$$r^2 = \frac{A_2}{\pi} = \frac{962.5}{3.1416} \approx 306 \quad \Rightarrow \quad r = \sqrt{306} \approx 17.5 \, \text{cm}$$​

2. Find the width of the ring:
Width = R - r = 21 - 17.5 = 3.5 cm

Final Answer:

The width of the ring is 3.5 cm.