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

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?

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.

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