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Solution for A Cylinder of Radius 12 Cm Contains Water to a Depth of 20 Cm. a Spherical Iron Ball is Dropped into Cylinder and Thus the Level of Water Raised by 6.75 Cm. Find Radius of the Ball. (Use 𝜋 = 22/7). - CBSE Class 9 - Mathematics

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Question

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball.
(Use 𝜋 = 22/7).

Solution

Given that,
Radius of cylinder= 12cm =`r_1` 
Raised in height =6.75cm=h 

⇒ Volume of water raised = Volume of the sphere

⇒ `πr_1^2h=4/3πr_2^3`

⇒ `(12xx12xx6.75)=4/3r_2^3`

⇒`(12xx12xx6.75xx3)/4=r_2^3`

⇒`r_2^3=729`

⇒`r_2=9cm`

Radius of sphere is 9cm.

  Is there an error in this question or solution?

APPEARS IN

 R.D. Sharma Mathematics for Class 9 by R D Sharma (2018-19 Session) (with solutions)
Chapter 18: Surface Areas and Volume of a Cuboid and Cube
Q: 15
Solution for question: A Cylinder of Radius 12 Cm Contains Water to a Depth of 20 Cm. a Spherical Iron Ball is Dropped into Cylinder and Thus the Level of Water Raised by 6.75 Cm. Find Radius of the Ball. (Use 𝜋 = 22/7). concept: Volume of a Sphere. For the course CBSE
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