A sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 13cm.If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel.

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0.84cm

0.83cm

1cm

0.99cm

answer is B.

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Detailed Solution

We have,
The sphere has diameter, d=6cmd=6cm
Thus the radius of the cylinder is r=3cm
The diameter of right circular cylindrical vessel is D=13cm.
Thus the radius of the circular cylindrical vessel is

Let the height of the rise in water level be ′h′.
Now, we can observe that the volume of water that will rise from its initial level will be equal to the volume of the sphere.
Therefore,

is the volume of the water level raised.
Vs is the volume of the sphere.

Therefore, from equation (1), we get

Substitute the given values in the above equation. We get
Question Image

We have the rise in water level will be 0.83cm(option2)
So, we write it as 0.83cm
So, option 2 is correct.

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