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Question
A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is 10 cm when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is 7 cm and height of the
cylinder is 20 cm.
Solution
Let the height of the water level be 'h', after the solid is turned upside down.
Volume of water in the cylinder
= `pi(7/2)^2 10`
Volume of the hemisphere
= `2/3pi(7/2)^3 `
Volume of water in the cylinder
= Volume of water level − Volume of the hemisphere
`pi(7/2)^2 10 = pi(7/2)^2h - 2/3pi(7/2)^2`
`=> 10 = h - 7/3`
`=> h = 10 + 7/3`
`=> h = 12 1/3 cm`
The height of water when the hemisphere is facing downwards is `12 1/3 cm`
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