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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. - Mathematics

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. (use `pi=22/7`)

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Solution

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

`:.1/3pir_1 ""^2h_1 = pir_2 ""^2h_2`

`:.r_1""^2h_1=3r_2""^2h_2`

 ∴ 5x5x24 = 3x10x10xh2

 

`:.h_2=(5xx5xx24)/(3xx10xx10)=2 cm`

Thus, the water will rise upto the height of 2 cm in the cylindrical vessel.

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