UPSC CDS I 2025 Mathematics Paper

Given:
The inside of the bowl is part of a sphere.
Depth of water (d)=d
Radius of the water surface =2d
Formula used:
Using the geometry of spheres, the radius of the sphere (R) is given by:
R=‌

(r2+d2)

2d

Where r= radius of the water surface =2d
Calculation:
‌R=‌

(r2+d2)

2d

‌⇒R=‌

((2d)2+d2)

2d

‌⇒R=‌

(4d2+d2)

2d

‌⇒R=‌

5d2

2d

‌⇒R=2.5d