A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

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Solution

In the given problem, we need to find the height of water in a given cylinder when a hemispherical bowl full of water is emptied into it.

Here,

Radius of the hemispherical bowl (r_s) = 3.5 cm

Radius of the cylinder (r_c) = 7 cm

So, according to the question, the volume of the water in the hemispherical bowl will be equal to the volume of the water in cylinder.

Let us take the height of the water level in cylinder as h cm

So,

Volume of hemispherical bowl = volume of the water in cylinder

Therefore, the height of the water in the cylinder is equal to .

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