CBSE Class 10 Math Question Paper 2016 | Q18

The given question is an easy 3-mark question from the chapter Surface Areas and Volume. Concept Tested: Computing volume of a sphere and a cylinder. It is an important question and appeared in Section C of the 2016 CBSE class 10 board paper.

Question 18: A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3\\frac{5}{9}) cm. Find the diameter of the cylindrical vessel.

Video Explanation

Explanatory Answer | CBSE 2016 Maths Paper Q18

Volume of sphere dropped = Volume of water displaced in the cylindrical vessel

Volume of sphere = \\frac{4}{3})πr³
Diameter of sphere = 12 cm; so, its radius = 6 cm
Volume of sphere = \\frac{4}{3}) × π × 6 × 6 × 6 ----(1)

Volume of water displaced = πr²h,
where 'r' is the radius of the cylindrical vessel and 'h' is the level by which water rises when the sphere is dropped
The height by which water has risen in the cylindrical vessel = 3\\frac{5}{9}) cm = \\frac{32}{9}) cm

So, volume of water displaced = π × r² × \\frac{32}{9}) ----(2)

Equate (1) and (2)
\\frac{4}{3}) × π × 6 × 6 × 6 = π × r² × \\frac{32}{9})
r² = \\frac{4}{3}) × 6 × 6 × 6 × \\frac{9}{32})
r² = 81 or r = 9
∴ Diameter of the cylindrical vessel = 18 cm