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: .