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Question

A sphere of diameter 12cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 359cm.. Find the diameter of the cylindrical vessel.


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Solution

Step 1: Finding the volume of the sphere

The diameter of the sphere=12cm

Therefore, the radius of the sphere=r=122cm=6cm

The volume of the sphere=43πr3

=43π63

Therefore, the volume of the sphere is 43π63.

Step 2: Finding the volume of the water rise in the cylindrical vessel

The height of water rise in the cylindrical vessel=359=329cm.

The volume of the water rise in the cylindrical vessel=πr2h

=πr2329

Step 3: Finding the diameter of the cylindrical vessel

If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 359cm.

The volume of the sphere=Volume the rise of water in the cylindrical vessel

43π(6)3=πr23294363=r2329r2=4×6×6×6×93×32r2=81r=81r=9

The radius of the cylindrical vessel is 9cm.

We know that the diameter of the cylindrical vessel is twice its radius .

Diameter of the cylindrical vessel=2×r

=2×9=18cm

Therefore, the diameter of the cylindrical vessel is 18cm.


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