UPSC CDS Math Volume and Surface Area Questions

Let the height of the cylinder is h and the radius is r; (h=2r) then V=πr2h
The maximum possible volume of sphere (radius R ) is immersed into cylinder if R≤r and 2r≤h
For maximum possible R=r=‌

h

2

When, we immersed the sphere into the cylinder the volume of water remains
‌‌=‌ volume of cylinder - volume of sphere ‌
‌‌=πr2h−‌

4

3

πR3
‌‌=2πr3−‌

4

3

πr3
‌‌=‌

2

3

πr3
‌‌=‌

1

2

×‌

4

3

πr3
‌‌=‌

V

3

‌‌[V=πr2h=2πr3]