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General

Easy

Question

# The area of a circular ring enclosed between two concentric circles is 286 cm^{2}. Find the radii of the two circles, given that their difference is 7 cm.

Hint:

### Radius of outer circle is the sum of radius of inner circle and difference between them.

## The correct answer is: 10 cm

### Let radius of inner circle be r

It is given that difference between the radii of both the circles is 7 cm.

Radius of outer circle – Radius of inner circle = 7 cm

Radius of outer circle = 7 + r

Further, it is given that Area of a circular ring enclosed between two concentric circles = 286 cm^{2}

We know that area enclosed between two concentric circles is the difference of the areas of two circles

Area of outer circle – Area of inner circle = 286 cm^{2}.

(r + 7)^{2} - p r^{2 } = 286

× ((r + 7)^{2} – r^{2 }) = 286

r^{2} + 7^{2} + 14 r – r^{2} = 91

49 + 14 r = 91

14 r = 91 – 49 = 42

r = 3 cm

So, radius of inner circle = 3 cm

Radius of outer circle = 3 + 7 = 10 cm

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