Question

please answer .........

Answer 1

Let the radius of outer circle be
$r_{1}$
Let the radius of inner circle be
$r_{2}$
Circumference of outer circle = 132 cm
$2\pi r_{1} = 132 \\ \pi r_{1} = \frac{132}{2} = 66 \\ r_{1} = \frac{66}{\pi} \: cm$
Circumference of inner circle = 88 cm
$2\pi r_{2} = 88 \\ \pi r_{2} = \frac{88}{2} = 44 \\ r_{2} = \frac{44}{\pi} \: cm$
Area of outer circle
$= \pi { r_{1} }^{2} = \pi \times \frac{66}{\pi} \times \frac{66}{\pi} = \frac{ {66}^{2} }{\pi} \\ = \frac{4356}{\pi} \: {cm}^{2}$
Area of inner circle
$= \pi { r_{2} }^{2} = \pi \times \frac{44}{\pi} \times \frac{44}{\pi} = \frac{ {44}^{2} }{\pi} \\ = \frac{1936}{\pi} \: {cm}^{2}$
Area of ring = Area of (outer circle - inner circle)
$= \frac{4356}{\pi} - \frac{1936}{\pi} \\ = \frac{2420}{\pi} \\ = \frac{2420}{ \frac{22}{7} } = 2420 \times \frac{7}{22} \\ = 110 \times 7 = 770 \: {cm}^{2}$
Area of Ring = 770 square cm.

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