RATIOS D1

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 = ∏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)

√(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.