UPSC CDS I 2025 Mathematics Paper

Let ' r ' be the inner radius of the circular opening of the pot.
Draw a vertical line from the center of the sphere to the center of the circular opening. This line segment will be perpendicular to the plane of the circular opening.
Let the center of the sphere be O . Let the center of the circular opening be C′.
The radius of the sphere (R) goes from O to any point on the surface of the sphere, including the edge of the circular opening.
Consider a right-angled triangle formed by:
The radius of the sphere (R) as the hypotenuse, from the center of the sphere to any point on the edge of the circular opening.
d=|R−hl=|20−30|=|−10|=10cm.
Now, substitute the values into the Pythagorean theorem:
‌R2=r2+d2
‌202=r2+102
‌400=r2+100
‌r2=400−100
‌r2=300
‌r=√‌300
‌r=√‌100×3
‌r=10√‌3cm