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 = πr\(^2\) 

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

Its area is πx\(^2\) .

x : r = 2 : 5,

so \(\frac{x}{r}\) =  \(\frac{2}{5}\)

 → 5x = 2r

Hence, x = 0.4r.

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

The ratio of the two areas is

0.16πr\(^2\) : πr\(^2\) 

 = 0.16 : 1 = 16 : 100

= 4 : 25.