Question

The area enclosed between two concentric circles is 770 cm². If the radii of the
circles differ by 7 cm, find both the radii.​

Answer 1

Let the radius of the inner circle = r

And radius of outer circle = R

Given :

Area enclosed between two concentric circles , A = 770 cm²

Difference of Radius = R - r

7 = R - r     { Given }

R = 7 + r ____(i)

Area enclosed b/w two concentric circles, A = Area of the Outer circle – Area of the inner circle

770 = πR² – πr²

770 = π(R² - r²)

770 = π((7 + r)² – r²)       { Putting value of R from (i) }

770 = π(49 + r² + 14r - r²)

770 = 22/7 (49 + 14r)

770 = 22(7 + 2r)

770 = 154 + 44r

770 - 154 = 44r

616 = 44r

r = 616/44

r = 14 cm  

Hence, the radius of the inner circle is 14 cm.

Putting value of r in (i) eqn;

R = 7 + 14

R = 21 cm

HOPE THIS HELPS YOU..

Answer 2

Let the radius of the bigger circle be R and that of the smaller one be r

$R-r=7cm\\ \pi R^{2}-\pi r^{2}=770\\  R^{2}-r^{2}=770/\pi =\frac{770*7}{22}=245\\ (R+r)(R-r)=245\\\frac{(R+r)(R-r)}{(R-r)}=245/7=35\\ R+r=35  \\ R-r=7$

Solving for R and r,

$R+r+R-r=35+7\\2R=42\\R=21\\r=14$

#BAL #answerwithquality