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 40 cm.
solution
let R = radius of larger circle
let r = radius of smaller circle
R= 40cm, 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) = (40/r)
5
= 40
2
r
(2 x 40) = (5 x r) after cross multiply.
80 = 5r
80
= 5r
5 5
r = 16
∴
radius of smaller circle is 16cm.
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.
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