AREAS A1

 The areas of the two circles are in the ratio of 49:4 . Calculate the radius of the smaller circle when the radius of the larger circle is 40 cm. 

 

Solution

 

let R = radius of larger circle

let r = radius of smaller circle

R= 40cm, r = ? Ratio = 49:4.

 

 

For larger circle

A1 = ∏R² …………(i)

 

For smaller circle

A2 = ∏r² …………(ii)

 

A1 = ∏R²

A2    ∏r²

 

A1 = R²

A2     r²

 

 

A1 = (R/r)² 

A2

 

√(^A1/A2) =  (R/r)

 

√(⁴⁹/4) =  (63/r)

 

7 = 63                 We cross multiply

2     r

 

(2 x 63) = (7 x r)   after cross multiply

 

126 = 7r

 

126 = 7r

7       7

 

r = 18

 

∴ radius of smaller circle is 18cm.

 

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.