Question

the radii of 2 circles are 13 and 5 cm what is the radius of the circle which has are equal to the difference of the are of the 2 circles

Answer 1

Hi,

Let R , r are radii of two circles ,

R = 13 cm ,

r = 5 cm

difference of the area of two circles

= π ( R² - r² )

= π[ 13² - 5² ]

= π ( 169 - 25 )

= 144π cm²

Let the radius of the new circle = r1

area of the new circle = 144π

π ( r1 )² = 144π

( r1 )² = 144π / π

r1 = √144

r1 = 12 cm

Therefore ,

required radius = ( r1 ) = 12 cm

I hope this helps you.

: )

Answer 2

Area of the first circle = πr^2. =22/7 × 13 ×13
= 531.142857cm^2
Area of second circle = πr^2 = 22/7 × 5 ×5
=78.5714286cm^2
Difference between both circle = 531.142857cm^2 - 78.5714286cm^2 =452.571428cm^2
So, the area of that circle = 452.571428cm^2
= πr^2 = 452.571428cm^2
= 22/7×r^2 = 452.571428cm^2
= r^2 = 452.571428 ×7/22
= r^2 = 144 cm
= r = √144
= r = 12 cm.