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If a circular paper disc is trimmed in such a way that its c...

If a circular paper disc is trimmed in such a way that its circumference is reduced in the ratio 2:5, In what ratio is the surface area reduced?

A.

8 : 125

B.

2 : 5

C.

8 : 25

D.

4 : 25

E.

4 : 10

Correct answer is D

surface area of formula = πr2 

If the radius is reduced then let its radius be x.

Its area is πx2 .

x : r = 2 : 5,

so xr25

 → 5x = 2r

Hence, x = 0.4r.

Hence the area of the new circle is π (0.4r)2  = 0.16π r2 .

The ratio of the two areas is

0.16πr2 : πr2 

 = 0.16 : 1 = 16 : 100

= 4 : 25.