This is a problem on mensuration ( VOLUMES AND SURFACE AREAS)

AI Thread Summary
The problem involves a right circular cone with a diameter of r cm and a height of 12 cm, placed on a right circular cylinder of the same radius, which is filled with water to a height of 12 cm. When the cone is removed, the volume of water left in the cylinder is calculated as πr²(12) - (1/3)π(r/2)²(12), resulting in a new water height of 11 cm. The discussion emphasizes the importance of clarity in calculations, suggesting that detailed steps should be shown for better understanding. It is also noted that the alignment of the cone and cylinder with the gravitational field is assumed for accurate results. The final conclusion is that the height of the water level after the cone is removed is 11 cm.
agnibho
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Homework Statement



A right circular cone of diameter r cm and height 12 cm rests on the base of right circular cylinder of radius r cm. their bases are in the same plane and the cylinder is filled with water up to a height of 12 cm. If the cone is then removed, find the height to which water level will fall

Homework Equations





The Attempt at a Solution



Radius of base of cone = r/2 cm Radius of the cylinder = r cm
Height of conical portion = 12 cm
or, Height of water in cylinder before cone taken out = 12 cm
Therefore, volume of water left in the cylinder when cone is taken out = πr2(12)- 1/3π(r/2)2*12 = πr2*11

Therefore, height of water left in cylinder = 11 cm
 
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Looks good to me!

(It would be better to show that calculation in more detail- I had to think for a minute to see how you got "11"!)
 
Thanks for the confirmation.
 
Assume, though not clearly unstated that, the axes of cone and cylinder are aligned with the gravitational field vector and the cone is on top, or answers will vary.
 

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