Angle of the cutout section = 4/100 *360 = 14.4 degrees
leftover perimeter = 96/100 * 2π * 25 = 48π
radius of cone bottom = 48π/2π =24 cm
sloping side of cone= radius of the original piece= 25
height² = 25²-24² =625 - 576
          = 49
height= 7 cm
radius:height =24:7
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only that method have i now
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SEE Diagram
when circular area of r =25cm is folded into a cone, the lateral length L of cone is = 25cm. as cone is formed by joining along the cuts.  Side Length of the cut is radius of circle.

Remaining Area of the circle of 25cm radius becomes the lateral area of the cone.
R is radius of base circle of cone.

So   0.96 π 25²  = π R L = π R 25
So    R = 24 cm.

Height²  = L²  - R²     This is because R L H form a pythagorus triangle.

Height = 7 cm

Ratio of radius to height is 24/7

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see diagram it will be easy.
thanx n u r welcom