A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (π = 22/7)

Let the radius of the conical vessel = r₁ = 5 cm
Height of the conical vessel = h₁ = 24 cm
Radius of the cylindrical vessel = r₂
Let the water rise upto the height of h₂ cm in the cylindrical vessel.
Now, volume of water in conical vessel = volume of water in cylindrical vessel
$therefore space 1 third straight pi subscript 1 straight r squared straight h subscript 1 space equals space straight pi subscript 2 straight r squared straight h subscript 2 therefore space straight r subscript 1 superscript 2 straight h space equals 3 straight r subscript 2 superscript 2 straight h subscript 2 superscript space therefore space 5 space straight x space 5 space straight x space 24 space equals space 3 space straight x space 10 space straight x space 10 space straight x space straight h subscript 2 therefore straight h subscript 2 space equals space fraction numerator 5 straight x space 5 straight x 24 over denominator 3 straight x 10 space straight x 10 end fraction space equals 2 space cm Thus comma space the space water space will space rise space upto space the space height space of space 2 space cm space in space the space cylinderical space vessel.$

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