Hello, snigdha!

A conical vessel of radius 6 cm and height 8 cm is completely filled with water.

A sphere is lowered into the water and its size is such that when it touches the sides,

it is just immersed. .What fraction of water will overflow? Code:

A 6 P 6 B
- o - - - - - - * o * - - - - - - o
:\ * | * /
: \ * |r * /
: \ * | * /
: \ | /
: \* oO */ 6
: \ | * r /
: * | * *
8 : * |r * *
: * | o Q
: \ * o * /
: \ | /
: \ | /
: \ | / 4
: \ | /
: \|/
- o
C

is the cone, with altitude

Its radius is: .

In right triangle , Pythagorus tell us: .

Note that: . . . Hence: .

The center of the sphere is with radius

In right triangle

We have: .

Then: .

The volume of the sphere is: .

. . This is the volume of water that will overflow.

The volume of the cone is: .

The fraction is: .