The given question is an easy 3-mark question from the chapter Surface Areas and Volume. Computing volumes of a cone and cylinder. This question appeared in Section C of the 2016 CBSE class 10 board paper.

Question 17: 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 π = \\frac{22}{7})).

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Volume of water in the conical vessel = \\frac{1}{3})πr^{2}h

= \\frac{1}{3})× π × 5^{2} × 24 ..... (1)

Let the height to which water will rise in the cylindrical vessel be 'h' cm

Volume of water emptied into the cylindrical vessel = πr^{2}h

= π × 10^{2} × h ..... (2)

**Equate (1) and (2)**

\\frac{1}{3}) × π × 5^{2} × 24 = π × (5 × 2)^{2} × h

\\frac{1}{3}) × 24 = 4 × h

or h = 2 cm

Class 10 Maths

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CBSE Class 10 Maths - 2022

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