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.

online.maxtute.com

Volume of sphere = \\frac{4}{3})πr^{3}

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 = πr^{2}h,

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 × r^{2} × \\frac{32}{9}) ----(2)

Equate (1) and (2)

\\frac{4}{3}) × π × 6 × 6 × 6 = π × r^{2} × \\frac{32}{9})

r^{2} = \\frac{4}{3}) × 6 × 6 × 6 × \\frac{9}{32})

r^{2} = 81 or r = 9

∴ Diameter of the cylindrical vessel = 18 cm

Class 10 Maths

Register in 2 easy steps and

Start learning in 5 minutes!

CBSE Class 10 Maths - 2022

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

Copyrights © 2016 - 22 All Rights Reserved by Maxtute.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

**Mobile:** (91) 93822 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@maxtute.com