JAMB - Mathematics (1978 - No. 14)
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?
8 : 125
2 : 5
8 : 25
4 : 25
4 : 10
설명
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.