# 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)

#### 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.

Concept: Concept of Surface Area, Volume, and Capacity
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