Question

A sphere of diameter 6cm is dropped into a cylindrical vessel partly filled with water.The diameter of vessel is 12cm.If the sphere is completely submerged in water how much water will be raised up?

Answer 1

Given diameter of sphere= 6cm
Therefore radius= 3 cm
Also given diameter of cylinder vessel = 12 cm
Therefore radius = 6 cm
Let the height of water raised = h cm
Now, volumn of water raised= volumn of sphere
22/7×6×6×h = 4/3×22/7× 3×3×3
Therefore h = 1 cm
1 cm of water will be raised up

Answer 2

Answer:

Given, diameter of speher = 6 cm

⇒ radius of sphere R=

2

6

=3cm

Diameter of cylindrical vessel = 12 cm

⇒ radius of cylindrical vessel = r=

2

12

=6cm

volume of sphere =

3

4

πR

3

=

3

4

π

2

(3)

2

Volume of cylindrical vessel = πr

2

h=π×6

2

×h

Here, the volume of sphere = volume increased in the cylindrical vessel.

∴

3

4

π(3)

3

=π(6)

2

h

h=

3

4

×

6

3

=

6×6

4×3×3

=

3

3

=1cm

∴ 1 cm level of water rise in the cylindrical vessel.