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Easy

Question

# The area enclosed by the circumference of two concentric circles is 364.5 cm^{2}. If the circumference of the inner circle is 88cm, calculate the radius of the outer circle.

Hint:

### Area enclosed by the circumference of two concentric circles is the difference of the areas of two circles.

## The correct answer is: 17.66 cm

### It is given that Circumference of inner circle = 88 cm

2 r = 88

2 × × r = 8

r = 14 cm

Let radius of outer circle = r_{1}

Area enclosed by the circumference of two concentric circles = 364.5 cm^{2}

i.e. Area of outer circle – Area of inner circle = 364.5 cm^{2}

(r_{1})^{2} - r^{2 } = 364.5

× (r_{1})^{2} - × (14)^{2} = 364.5

((r_{1})^{2} – 14^{2}) = 364.5

((r_{1})^{2} – 14^{2} =

(r_{1})^{2} = 311.977

r_{1 } = 17.66 cm

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