The areas of
two circles are in the ratio of 25:4 . Calculate the radius of the smaller
circle when the radius of larger circle is 50 cm.

__solution__
let R =
radius of larger circle

let r =
radius of smaller circle

R= 50cm, r =
? Ratio = 25:4.

For larger
circle

A1 = ∏R

^{2 }…………(i)
For smaller
circle

A2 = ∏r

^{2 }…………(ii)__A1__=

__∏__R

^{2}

A2 ∏r

^{2}__A1__=

__R__

^{2}

A2 r

^{2}__A1__= (R/r)

^{2 }

A2

√(

^{A1}/A2) = (R/r)
√(

^{25}/4) = (50/r)__5__=

__50__cross multiply

2 r

(2 x 50) =
(5 x r)

100 = 5r

__100__=

__5r__

5 5

r = 20

__∴__

__radius of smaller circle is 20cm.__

__TRY THIS………..__
NECTA 1997
QN 5(c)

The areas of
two circles are in the ratio of 16:9 . Calculate the radius of the smaller
circle when the radius of larger circle is 24 cm.