A cylinder of radius 12 cm and height 28 cm is kept on top of an inverted cone which is covered with a lid.The height of the cone is 33.33% more than its radius.Then the cylinder is filled with water upto a height of 14 cm and the lid is removed such that the top of water level forms a circumference of 6pie.Find he final level of water in the cone?
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In the cone, water is up to a level of 4 cm.
Let,
- radius of cylinder, R = 12cm
- height of cylinder. H = 28cm
- Radius of cone, r = 12cm
- Height of cone, h = 12 + (12*33.33%)cm = 12 + 3.9996cm = 15.9996cm ≈ 16cm
After the lid is opened, water falls into the cone and the surface water occupies a circumference of 6π cm
- Circumference = 6π cm ⇒ 2πr' = 6π cm ⇒ r' = 3cm [ where r' is the radius of water surface in cone ]
By, Thales' theorem,
- r'/r = h'/h ⇒ 3/12 = h'/16 ⇒ h' = 4 cm [ where h' is the height of water surface in cone ]
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