Question

The area of two circles with same center are 154sq cm and 616sq cm then the width of the concentric circle is​

Answer 1

Answer:

$\red {, Width \: of \: concentric \:circle}\green {= 7 \:cm }$

Step-by-step explanation:

$Let \: radius \: of \: the \:inner \:circle = r\:cm$

$Area \:of \:the \:inner \:circle = 154 \:cm^{2}$

$\implies \pi r^{2} = 154$

$\implies \frac{22}{7} r^{2} = 154$

$\implies r^{2} = 154 \times \frac{7}{22}$

$\implies r^{2} = 49$

$\implies r = 7 \:cm$

$Let \: radius \: of \: the \:Outer \:circle = R\:cm$

$Area \:of \:the \:Outer \:circle = 616 \:cm^{2}$

$\implies \pi R^{2} = 616$

$\implies \frac{22}{7} R^{2} = 616$

$\implies R^{2} = 616 \times \frac{7}{22}$

$\implies R^{2} = 196$

$\implies R = 14 \:cm$

$Now , Width \: of \: concentric \:circle = R-r\\= 14 \:cm - 7 \:cm \\= 7 \:cm$

Therefore.,

$\red {, Width \: of \: concentric \:circle}\green {= 7 \:cm }$

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