Question

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The difference of areas of two concentric circle is 286 cm2 and the difference of their radii is 7cm. Find the radius of each circle​

Answer 1

Answer:

Area of a circle = πr^2

Concentric circles are those whose center is same.

Let the radius of bigger circle = R

Let the radius of smaller circle is = r

According to Question,

πR^2 - πr^2 = 286 cm^2

π(R^2 - r^2) = 286

R^2 - r^2 = (286/22)11

R^2 - r^2 = 91 ----------(I)

The difference of their radii is 7 cm

R - r = 7 cm

R = 7 + r cm -----------(2)

Putting the value of R in the equation (1)

(7+r)^2 - r^2 = 91

49 + r^2 + 14r - r^2= 91

14r = 91-42

r = 42/14

r = 3 cm

Putting this value in equation (2)

R = 7 + 3 = 10 cm

So the radii of bigger circle is 10 cm and the smaller circle is 3 cm.

HOPE IT HELPS YOU.