CBSE Class 10 Math Question Paper 2016 | Q17

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})).

Video Explanation

Explanatory Answer | CBSE 2016 Maths Paper Q17

Volume of water in the conical vessel = Volume of water emptied into the cylindrical vessel

Volume of water in the conical vessel = \\frac{1}{3})πr²h
= \\frac{1}{3})× π × 5² × 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 = πr²h
= π × 10² × h ..... (2)

Equate (1) and (2)
\\frac{1}{3}) × π × 5² × 24 = π × (5 × 2)² × h
\\frac{1}{3}) × 24 = 4 × h
or h = 2 cm