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प्रश्न
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`)
उत्तर
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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Solution :
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∴ The surface area of the sphere = `square` sq.cm.
