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

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

A.

2.1 cm

B.

1 cm

C.

5.5 cm

D.

3.5 cm

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=πr2A = \pi r^2
For the two circles:
A1=πR2andA2=πr2A_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:
R2=A1π=13863.1416441=>R=441=21 cmR^2 = \frac{A_1}{\pi} = \frac{1386}{3.1416} \approx 441 \quad \Rightarrow \quad R = \sqrt{441} = 21 \, \text{cm}
r2=A2π=962.53.1416306=>r=30617.5 cmr^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.

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