Question

the sum difference of the radii of two circles is 140 `cm and the difference of the circumference is 88 cm. find the ratio between the areas.

Answer 1

Solution is attached below in image

Answer 2

Answer:

$Ratio\: of \: Areas = \frac{121}{81}$

Step-by-step explanation:

Let R and r are radii of two circles .

$Given R+r = 140\:---(1)$

$and\\Difference \: of \: their \:circumstances =88\:cm$

$\implies 2 \pi R - 2\pi r = 88$

$\implies 2\pi (R-r) = 88$

$\implies 2\times \frac{22}{7} \times (R-r) = 88$

$\implies R-r = 88 \times \frac{7}{44}$

$\implies R-r = 14 \: --(2)$

/* Add equations (1) and (2), we get

$2R = 154$

$\implies R = \frac{154}{2}=77$

Substitute R=77 in equation (1) , we get

r = 63

Now ,

$Ratio\: of \: Areas = \frac{\pi R^{2}}{\pi r^{2}}$

$= \frac{R^{2}}{r^{2}}\\=\left(\frac{R}{r}\right)^{2}\\=\left(\frac{77}{63}\right)^{2}\\=\left(\frac{11}{9}\right)^{2}\\=\frac{121}{81}$

Therefore,.

$Ratio\: of \: Areas = \frac{121}{81}$

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